Un Paused

When somebody is frozen in the middle of an action, they will always resume right where they left off in the middle of the action, often with hilarious results. May be a Brick Joke.

When something is paused in the middle of a physical motion (as by magic), it sometimes retains its momentum when it's unpaused and sometimes loses it, usually depending on what would be funny or cool.

Often a result of Time Stands Still. Can overlap with Waking Non Sequitur.

Examples of Un Paused include:

Anime and Manga

Used extensively in Code Geass, where Rolo's Geass stops time (or close enough). Once unpaused, characters continue to fight in their mechas, monologue, or beg intermittently for Rolo to stop using his Geass.
A variation occurs in One Piece with Foxy's NoroNoro Beam, which allows him to slow down people/objects for 30 seconds. While slowed down, the target will appear to be doing the same thing, even if, say, a huge, powerful fist flies right into their face.

Comic Books

Not played for laughs in an issue of Planetary where a dead woman is successfully revived, and finishes what she was doing when she died: screaming.
In an issue of Excalibur, the team is fighting a team of interstellar mercenaries when two other characters show up and temporally freeze the mercenaries so they can conduct some unrelated business with Excalibur. The freeze wears off about five minutes later... by which point Excalibur has moved them around such that their unpaused attacks are aimed at each other.

Film

In Rango, Beans has occasional catatonic fits. When she snaps out of them, she continues with whatever she was saying as if nothing had happened. Sometimes it's entirely different topics, such as Alien Abduction.
Batman: The Movie. The United World Security Council members are dehydrated while they're arguing with each other around a conference table. While dehydrated their molecules were mixed together, separated and thoroughly scrambled. When they're rehydrated they immediately pick up where they left off. Watch it here.
The Empire Strikes Back. C-3PO is damaged by Imperial stormtrooper fire. When he's repaired and reactivated, he replays what he was saying and thinking when he was attacked.

C-3PO: I'm terribly sorry. I didn't mean to intrude. No, please don't get up. Stormtroopers? Here? We're in danger. I must tell the others. Oh, no! I've been shot!

In the film Support Your Local Sheriff, James Garner escapes a brawl at a restaurant by yelling "Hold it!" and quietly stepping to one side, taking his food with him. Once he's out of harm's way, he says "Okay, go ahead on!" and the brawl resumes exactly where it stopped.
In the film version of Ella Enchanted, Ella is frozen mid-leap over a puddle, and when she's unfrozen she falls into the mud.
In Jurassic Park, Tim is in the middle of counting to three before getting zapped unconscious by the perimeter fence. Upon waking up, he finishes: "...three."
In Kung Pow: Enter The Fist, the movie freezes just as Betty is about to hit Master Tang with his claws. Tang then narrates:

Master Tang: Ok, so here were my options. a) quickly duck left, dodge the claw and take him out with a spinning back kick, or b) take the claw in the face, roll on the ground and die. (unpause) Hmm, should've gone with a.

In The Mask the titular superhero responds to a order to "Freeze!" by doing exactly that—stopping dead in midair, covered in icicles. When told by the exasperated cop to "Unfreeze" (because otherwise he can't obey a further order to put his hands up), he finishes his leap and gets tackled by the cops.
This happens a few times in the X Men films, thanks to Professor X's ability to "pause" people with telepathy.

Literature

Older Than Radio: In the Brothers Grimm's "Briar Rose" (a.k.a. Sleeping Beauty), when the princess pricks her finger the entire castle falls asleep instantly; the cook in the palace kitchens falls asleep in the act of boxing the kitchen boy's ears, and finishes delivering the punishment one hundred years later when the castle wakes up.
Near the end of The Colour of Magic Rincewind and Twoflower's current captor uses a spell to freeze in midair a bottle hurled towards him, arresting its momentum. Eight hours later, when the spell wears off, he happens to be standing in the same spot... (Note that in TCOM this is intentional; the deity that the protagonists are speaking with specifically manipulates the laws of chance so that the bottle just happens to be in the exact place and time to hit the guard and allow them to escape.)
Robert Heinlein's Starship Troopers. When Johnny Rico is put to sleep via post-hypnotic suggestion and then woken up again, he doesn't realize he's been asleep for more than an hour. He continues talking to the commanding officer who put him to sleep as if it hadn't happened.
One trait of the aliens in Harry Harrison's story "The Streets of Ashkelon" is that they resume interrupted conversations in mid-stream even if days have passed since the interruption. Obviously, they have better (or at least differently-wired) memories than humans.

Live-Action TV

In the first episode of Pushing Daisies, the first thing Chuck does after Ned brings her back to life is grab his tie and bang him on the lid of her coffin in self-defense against her killer.
This was the entire schtick of the paralyzing horn in El Chapulin Colorado.
The episode of The Twilight Zone entitled "A Kind of a Stopwatch" has this in it, until the stopwatch breaks.
In the The Man from U.N.C.L.E. episode "The Brain Killer Affair", Illya is zapped with some kind of hypnosis device just as he's about to make a call on his cigarette-case radio. When Napoleon snaps him out of the resulting catatonic state hours later, he immediately starts talking into the radio.
There's a scene in Eureka where Beverly is hypnotizing Fargo. She gives the standard end-of-hypnosis "when I snap my fingers, you will return to normal and forget all about this" speech and snaps her fingers, causing him to finish explaining to her exactly why hypnosis is impossible.
In The Dick Van Dyke Show episode "My Husband is Not a Drunk" Buddy is in the middle of explaining that he can't be hypnotized, then gets hypnotized. When he gets snapped out he continues his sentence about being unhypnotizable. Subverted though, in that Buddy was only pretending to be hypnotized.
Happened to the holographic Doctor in Star Trek Voyager when Seven switched him off in the middle of a sentence.
There is an early (season 1 or 2) episode of House where a patient is having seizures. He will stop in the middle of a sentence for a few moments before going right back to what he was saying, unaware that he lost any time.
Done hilariously in the notorious train episode on Due South. An entire train car full of Mounties is gassed and pass out while singing early in the episode. Right before the climax, every single one of them wakes up simultaneously, at which point they resume singing the chorus.
Red Dwarf
- Episode "Pete: part 1". Kryten, Kochanski and the Cat come upon a team of Canaries frozen by the Time Wand. When Kryten tries to fix them, they instead intermittently unpause.

Canary: Don't mess... (long pause) with that thing, it can re... ally screw... ew-ew-ew... you up!

- Later, they use the Time Wand to freeze the entire crew, including a pair playing ping-pong who, when later unfrozen, suddenly find the ball they had in mid-air was suddenly missing because Lister had taken it away while they were frozen.
Saved by the Bell has a Running Gag where Zack would say "Time out!", causing the other characters to freeze in place. Although this was normally only used only to address the audience, Zack wasn't above occasionally messing with the scene while it was frozen, such as using it to escape a punch (Mr. Belding, who had been behind him, got hit instead).
Stargate SG-1
- At the beginning of the episode "Urgo", the team is going through the Stargate while O'Neill is making some joking aside. When they emerge from the event horizon, O'Neill is pursuing his dialogue... except they're back at the SGC after a three-hour timelapse, and have no memory of visiting another planet.
- There is also the running gag of someone (usually O'Neill) being teleported mid-sentence by the Asgards. Upon arriving on the alien ship or back on Earth, they usually conclude whatever they were saying before looking around in annoyance.

Music Videos

In the clip for "Blue (Da Ba Dee)" by Eiffel 65, the singer is abducted by aliens in a stasis sphere during a concert. When he's released on their planet, he immediately resumes singing, although his audience is now entirely composed of blue aliens.

Professional Wrestling

Player Uno of CHIKARA uses this as part of his gimmick, as shown in these clips.

Tabletop Games

Paranoia supplement Acute Paranoia, adventure "Me and My Shadow Mark IV". Markie (the Mark IV warbot) is talking to the PC's when a piece falls off of him, sending him into a catatonic state. When the piece is re-attached, Markie continues talking right where he left off.

Video Games

In The Curse of Monkey Island, Elaine is gearing up to punch Guybrush right before she is turned into a statue. Once revived, she floors him. (Granted, he had it coming).
The frozen Gadgetron scientist in Ratchet and Clank Going Commando. When broken free from his ice block he's still celebrating the success of his Thermanator (which froze him in the first place). "It worked! It worked!"
In Borderlands' fourth DLC, the claptrapped version of Commandant Steele, who died at the end of the main game finshes the speech she was giving before being impaled by the Giant Space Flea From Nowhere Final Boss.
Sonic Generations opens with the villain apparently destroying time and space, banishing Sonic into a white limbo, kidnapping most of the extended cast, and blasting a chili-dog out of Sonic's hand. Upon restoring the world, Sonic's first action? Catch the falling chili-dog.

Web Comics

In The Order of the Stick, Haley is petrified in mid-sentence, then finishes the sentence when she's restored 30 strips later.

Web Original

Double Subverted in Doctor Horribles Sing Along Blog. The title doctor freezes Captain Hammer right before his song's big finish. When he's unfrozen, he punches the doctor in the face, and then finishes his line.

Western Animation

In the first episode of Futurama, Fry pushes Leela into a stasis pod mid-lecture, and sets the release time for later that day. When she comes out later she's still yelling at him.
In the Justice League episode featuring Deadman, Superman gets possessed midsentence while talking about a restaurant in Smallville where "the milkshakes are so thick..." When he regains control of his body, Supe's first words are "...you have to eat them with a spoon! (glances around) Why am I in Africa?" What makes the exchange even funnier is that, at the moment of possession, the first thing Deadman uses Superman's body to say is "I need your help," prompting odd glances from Batman and Wonder Woman. That's pretty thick, indeed.
During an episode of Voltron Force, King Lotor, hopped up on haggarium, declares that "This is the day that I-" and gets blasted by Voltron's new guns. When he is later revived back at his castle, the first thing he says is "-destroy Voltron!" ... and smacks face first into a wall.
Played with in Harvey Birdman, Attorney at Law. In a spoof of the old Birdman cartoon, Phil is frozen mid-sentence: "A madman is freez--". When Birdman unfreezes him: "Ha ha ha, --ing!"

Real Life

It is said (but not true) that when the BBC started broadcasting again after World War II, it picked up from the same place in a cartoon where it had stopped... The TV transmitter was shut down in the middle of a Mickey Mouse cartoon. After the war the television service did apparently resume with the same cartoon, but from the start.
Jack Paar left The Tonight Show on-air to protest the censoring of a joke. He said,

"I've made a decision about what I'm going to do. I'm leaving The Tonight Show. There must be a better way to make a living than this, a way of entertaining people without being constantly involved in some form of controversy. I love NBC [...] But they let me down.

After he was convinced to return almost a month later, he began his monologue with...

"As I was saying before I was interrupted... I believe the last thing I said was 'There must be a better way to make a living than this.' Well, I've looked... and there isn't."

One of the better-known variations of a Flashmob involves everyone showing up at a certain time and pretending to freeze for a few minutes, after which this trope is invoked.