Left Your Lifesaver Behind

A character rushes out of the room and a closeup shot reveals they've left their firearm behind, or some other crucial item like a mobile phone or the Amulet of Dependency. Naturally they're heading right into a situation where they'll need it.

Not related to Leave Behind a Pistol.

Examples of Left Your Lifesaver Behind include:

Anime and Manga

Gunslinger Girl. Cyborg girl Triela runs away in tears after realising her handler went on an assassination mission without her and got wounded in the process. She leaves both her pistol and conditioning medicine behind, and withdrawal symptoms make her too weak to defend herself when she gets grabbed by a couple of Camorra thugs.

Film

Invoked in Sherlock Holmes. Watson is furious when Sherlock leaves without his revolver, knowing he did it deliberately so his friend will feel obliged to chase after him.
The Sure Thing. When Gib and Allison leave the hotel room, Allison accidentally leaves her all-important planner (which contains all her money) behind.
Pulp Fiction. Vincent is waiting at Butch's apartment to kill him if he shows up. While waiting, Vincent needs to go to the bathroom, so he leaves his Ingram MAC-10 on the kitchen counter. While he's in the bathroom, Butch shows up, and uses the Ingram to kill the unarmed Vincent as he leaves the bathroom.
While on the way to fire off the flares needed to destroy the titular giant spider in Giant Spider Invasion, Dr. Vance forgets the flares and needs to run back to the car and get them. Mike and the Bots immediately call out how dumb this was, since it doesn't add any real tension and only pads out an extra 10 seconds or so of running time.

Literature

The non-fiction book by David Simon, Homicide: A Year on the Killing Streets mentions that detectives have to remind themselves to take their guns with them, as real life officer-involved shootings are a rare event.
Subverted in The Silence of the Lambs. When Clarice Starling goes to see Dr. Lecter in Tennessee, she has to turn over her spare reloader for her revolver. When she's discovered and rushed out, she leaves her reloader behind. If you noticed this and were Genre Savvy, then during her final confrontation with Buffalo Bill, you were expecting her to run low (or out) of bullets, look for her reloader and not find it, and have to defeat Buffalo Bill with just One Bullet Left or an empty gun. In fact, she finishes off Buffalo Bill with several shots and then reloads.
Parasite Eve has Aya go to confront the final boss right before another character would have given her the one weapon that could kill it. Though to be fair, this character had a habit of giving Aya useless items, and there was no way for her to know that this one time, it was important.
Slightly different example in A Song of Ice and Fire. While a group of people are escaping from Ramsay Bolton, with a plan that requires them to climb down the castle wall with a rope, they get discovered, and one of them decides to pull a Heroic Sacrifice You Shall Not Pass on the guards chasing them to let the others escape. They go ahead and reach the top of the wall...only to realise that the person who stayed behind had the rope. Despite one of them bursting into hysterical laughter at the absurdity of it, this is very much Played for Drama.

Live Action TV

Ultraviolet. The protagonist rushes out to meet his Unrequited Love Interest, taking his pistol but forgetting the video camera attachment used to identify vampires. This causes problems when he starts suspecting she's a vampire, but has no means of verifying it.

Western Animation

One of the Treehouse of Horror specials of The Simpsons had a Nightmare On Elm Street spoof with Groundskeeper Willie as Freddy Kruger. After the Simpsons kids kill the evil Willie in their dreams, they go outside and an alive and well Willie gets off a passing bus and approaches them menacingly—only to start chasing after the bus because he says he left his gun on it.