Bob is devoured by a monster. Monster looks pleased at its victory and goes to eat Alice. Alice is terrified until the monster stops, gives her an odd look, and screams as Bob cuts his way out of its stomach.
If Bob had yelled "Eat Me!" moments before, then he was almost certainly planning to do this, and obviously, it doesn't work unless said monster swallows people whole. Let that be a lesson to all you monsters out there: always chew your food properly.
See also Chest Burster, Just Eat Him, and Feed It a Bomb. Not to be confused with Through His Stomach.
In Rosario + Vampire, Moka is eaten by a plant monster. Inner Moka then literally kicks her way out of the monsters stomach.
Near the start of the Sazan Eyes is a variation. Yakumo doesn't really have any powers yet, but manages to kill a monster (temporarily anyway) by shoving a summoning staff into its mouth and summoning Takuhi inside it to burst its stomach from within.
Naruto was once swallowed by a gigantic snake summoned by the Big Bad. He escaped by making so many clones of himself that it burst.
In Frankenstein: Agent of S.H.A.D.E. Frankenstein is swallowed by a mountain sized monster. A page later he bursts out of it's body with his sword in one hand and it's heart in the other. The "why didn't it chew him" factor is justified here as the creature is so gargantuan Frankenstein's not much more than a crumb to it.
Wolverine kills the mutant killing monster Predator-X this way. In this case, the monster may have chewed him a bit, but his Healing Factor could easily fix that.
The dragon scene from The Pagemaster. After Richard is eaten by a dragon, he makes a beanstalk appear by opening a book entitled Jack and the Beanstalk that was also inside the dragon's stomach, and uses it to escape.
Film - Live-Action
In the Hellboy movie, HB kills the monster at the end by letting the monster grab him, and yanking the pins out of an entire belt of grenades just before the monster swallowed.
K in Men In Black does this when he talks the giant alien cockroach — who had earlier eaten both his and J's guns — into swallowing him whole. His explanation to J prior to doing this was "I'm goin' to get my gun back." He does, and proceeds to blast said giant alien cockroach in two from the inside out.
The alien assassin from Men In Black II is tricked into flying down Jeff the giant worm-creature's gullet, but grows large enough to burst out of him for a final battle with J.
Piper and Grams from Charmed were once eaten by the Big Bad Wolf. Piper uses her power to blow the fairy tale beast to smithereens while she was still inside of it.
Earlier in the series Piper's plan to defeat a demon was to let it eat her and her sisters and then Prue would use her powers to blow it up. Fortunately, they didn't have to do it this way.
While it's unclear whether Buffy was actually ingested by the monster, in one episode she defeats this mother of body snatching beasts by slicing it with a pickaxe, presumably from the inside out.
In the Golden Legend, this is how Saint Margaret of Antioch survived her first martyrdom phase. She was to be eaten alive by a huge snake (for some, Satan in the form of a dragon), but her cross pendant irritated the dragon/snake's innards and it bursted open, with an unharmed Margaret popping out of it.
In Dungeons & Dragons, PCs that get eaten by huge monsters sometimes have to cut their way out. Sometimes it's actually a good idea, as its stomach does less damage than its outside.
This was completely and hilariously averted in 3.0 and 3.5, where any number of things (Tyrannosaurs, giant sharks, purple worms) could swallow you whole, requiring you to cut your way out... but slicing a giant hole in the critter didn't deal any actual damage to it, and "Once the creature exits, muscular action closes the hole; another swallowed opponent must cut its own way out."
One Spelljammer module has a gammaroid (colossal turtle) who met a primary Witchlight Marauder. Which is the first stage of an artificial Horde of Alien Locusts — it's designed to spawn monsters that end up stripping a whole planet of everything organic. Gammaroids in average are five times bigger than this, so the turtle had a nice snack. Then secondaries hatched. All that remained is an enormous shell with bones inside.
Savvy players will elect to attack the giant beast's heart or other internal organs while inside, and presumably after cutting through its stomach. Your GM will have to decide how well it works.
Halfway through the first boss fight in The New Zealand Story, the ice whale you're fighting swallows you. You have to shoot it while avoiding the drops of acid in order to destroy it from within.
In Tales of Legendia, the largest monsters in the game are too big for Senel to throw, so instead of throwing them, he'll invoke the trope by jumping into their mouths and pummeling them from the inside while they're dazed from being knocked down.
During one boss fight in Yoshi's Island, Yoshi and Baby Mario are shrunk and eaten by a frog. You then "defeat" the frog from within its stomach by throwing eggs at a uvula-like appendage.
The Riftworm in Gears of War 2 meets its end after swallowing the protagonists, who return the favor by making their way through its body and cutting out its hearts.
In the Flash game "The Visitor", the alien's first victim is a frog who thinks it looks tasty and slurps the little guy up with its tongue. The frog explodes a second later, and the alien is noticably larger. The visitor later flies into a sleeping guy's open mouth. He doesn't fare any better than the frog.
Red Mage does this to a dragon in 8-Bit Theater using frost magic. Interestingly the dragon was only acting in self defence and was perfectly happy to help the remaining Light Warriors when they didn't attack. Indeed RM killed him half way through making them some fireproof armour.
Later, he defeated Kraken this way, bisecting him from the inside with his sword.
In The Order of the Stick, V gets eaten by a dragon, and uses a Shapechange spell to burst their way out... appropriately enough, by transforming into a dragon.
Schlock Mercenary had a mild version with some amphibious monster chomping Tagon in the middle of his talk about security. The critter had just enough of time to worry about the leg in Powered Armor in can't bite through before Tagon used his sidearm to make a new exit out of its mouth.
Adventure Time: Finn must slash his way out of the gullet of a… something, after Marceline tells him, "Use my axe bass."
Duck Dodgers employs a non-lethal version of this trope, Played for Laughs naturally. Daffy, unable to beat the enemy (played by Taz), decides the best answer is cooking himself, then serving himself up to his foe explicitly saying "Eat me!" After this, he proceeds to stand up fully inside Taz's stomach. Complete with obligatory Lampshade Hanging, but not in the usual manner. See the scene in it's entirety here.
In the Planet Hulk animated film, the angry green giant himself jumps into the flaming mechanical jaws of a robot worm only to pop out minutes later though its chest tearing out, what could be assumed to be, its intestines with it.
Some species of pufferfish are covered with spikes which bristle in all directions when the fish puffs up, making it nigh impossible to take a bite of. Larger predators, however, can swallow it whole... after which it will try to gnaw its way out with its sharp beak, usually successfully. Notably, critters who manage to digest the pufferfish before it gives them a Torso with a View don't fare well either, as pufferfish are among the most poisonous creatures in the world.