From Dress to Dressing

When miles away from a first aid kit, your jammies will do

Somebody is injured and there is no hospital, drugstore, or first aid kit in sight. This leaves only one option, someone is going to have to rip up the clothes they are wearing to make a bandage to put on that wound.

This is an action that, though seemingly a simple act of kindness, can say many things about the characters involved. It can show that if they don't hesitate at all the character ripping their clothes is either a battle or survival pragmatist, or if they do hesitate that they are perhaps a tiny bit vain or at least image conscious or if said clothes were expensive and / or new they are more mindful of the money they are wasting rather than the needs of others.

It also can be can be used to send romantic signals about the characters involved, it is not uncommon to have the person ripping the clothes being a girl and the injured party be a guy she likes. The fact that it is commonly a woman doing this can be seen as a form of mild titillation if it is played for Fan Service.

Examples of From Dress to Dressing include:

Anime and Manga

Sailor Moon Naru does this with her pajamas to make a bandage for Nephrite when they are hiding from Zoisite in a park after his attack. She hangs onto said bandage as a token to remember him by after he dies and eventually uses it on a wound Umino gets whilst trying to defend her to show she's moved on emotionally from Nephrite's death.
Captain T-Bone from One Piece does this for using his own clothes for his men even if his men's injuries aren't that serious.
In the second season of "Attack on Titan" Krista does this for Reiner after his arm is injured.

Film

Janet ripped her slip to make a bandage for Rocky in The Rocky Horror Picture Show just before the "Toucha Toucha Toucha Touch Me" number.
- He's got more hurt than you've got skirt!
Parodied in Hot Shots: Part Deux, the main girl rips off a part of her (already scant) clothing to bandage a wounded team member, then another one, then the resident perv realizes she'll just keep going until she is completely naked, so he claims he is wounded, too.
In the early Michael J. Fox movie Doc Hollywood, he momentarily agonizes over having to rip up some Armani shirts in order to treat a woman who's gone into sudden labor.

Literature

In the second Dragonriders of Pern novel, F'lar and Lessa are wearing new outfits to a wedding. F'lar ends up in a duel with T'ron, during which he gets his suit cut up, and Lessa has to rip up her dress to make bandages.
In the 1924 novel Jungle-Born by John Eyton a village girl who's run away from her abusive father finds the Wild Child protagonist unconscious and badly injured from a tiger attack. To save him she strips off her one and only garment and tears it into strips to wash and bandage his wounds. The fact that this means they're now both naked probably isn't insignificant.
Most Tamora Pierce books include this.

Live Action Television

There was an episode of The Flying Nun where Sister Bertrill tore her habit to make a bandage.
An episode of Gunsmoke had Kitty shred up her petticoat to make bandages for an ailing Matt.
Survivorman Les Stroud has done this after injuring himself in the wild.
In Upstairs, Downstairs (2010) Lady Agnes Holland uses an expensive looking blouse to stem the bloodflow of Beryl, after Lady Persephone shoots her and then kills herself, she even tells the staff to ignore Lady "Persie" who is already dead.
Star Trek, particularly Deep Space Nine, did this several times: the characters would find themselves without their advanced medical technology, so they (usually Bashir) would rip up their uniforms to make bandages.
Angel. After bandaging Wesley when he gets an Impaled Palm from a Booby Trapped door, Cordelia points out that she doesn't have enough shirt for the rest of them.

Video Games

In the final part of Mass Effect 3, you can hear a man instructing a girl to do that over the radio.

Western Animation

Not clothing, but thematically similar, in My Little Pony Friendship Is Magic Rarity cuts off her tail to fix the mustache of "Steven Magnet" the sea-serpent who is suffering a Minor Injury Overreaction. It's done specifically to highlight how her generous nature outweighs her fashionista personality to set her up as the wielder of the Element of Generosity.
Used for humorous Fan Service in the Archer episode Space Race Part 2. While being held hostage on a space station, Lana Kane opens her jumpsuit and removes her tank top to distract the guard so she and the rest of the ISIS hostages can overpower him. In an offscreen fight Lanas jumpsuit is destroyed and Archer is shot in the arm. Left wearing only panties, Lana reaches for her tank top just as Archer is wrapping it on his arm as a bandage. This leaves Lana with nothing but space agency decals to cover her nipples with.

Real Life

In the case of Real Life of it happening... in the past it has happened on the battlefield before First Aid Personnel were commonly deployed, and can happen now. But also take a zone after any disaster and you cannot locate a First Aid kit, therefore you use clothes as a makeshift bandage.
Readers Digest wrote about one of those incredible true stories of the one hundred pound girl dragging her six foot injured boyfriend down a mountain. She stripped over her jacket to wrap a gash on her leg, her bikini top for his head wound, and said that, "If the bottom half [of the bikini] had to come off too, it would have." Props, lady.