Biography
An odd sort of polar opposite to The Woobie, The Chew Toy is a character the audience loves specifically because their misery amuses them so. The Chew Toy is roughed up or messed with on a constant basis... and is always, always used for comic effect and treated with a light touch, generally glossing over the meaner undertones of the idea.
Whatever the reason is, these characters just can't catch a break. Did they do something wrong in a previous life? This life? Or are they just Innocent Bystanders who look as if they'd blow up in a more amusing manner than anyone else in the crowd? Who knows. Either way, the powers that be tend to inflict punishment on them for seemingly no reason, generally but not always of the slapstick physical variety.
Unlike Woobification, Chew Toys are generally designated as such in the series proper, and often have a tendency to bemoan their fate. If they're lucky, the writers will Throw the Dog a Bone a time or two. If they're unlucky, they'll Yank the Dog's Chain. It can sometimes be a delicate balance. Throw too often and the character can be Flanderized into The Eeyore; Yank too much and the audience may no longer find it funny. The latter will happen mostly if the character is both deliberately and unfairly mistreated by other characters.
Compare Butt-Monkey (a character who is mistreated regardless of audience opinion), The Eeyore (whose depression is usually in excess of their actual mistreatment) and Iron Butt-Monkey (who seems to suffer injury and accidents more frequently than anyone should, but is capable of taking it). Contrast The Woobie, whose suffering inspires sympathy and a desire to make things better for them instead of amusement.note The polar opposite is Karma Houdini, where characters do horrible things while karma (and occasionally the other characters) sits back, watches, and eats popcorn. Villains and Unsympathetic Comedy Protagonists, though, do make good Chew Toys as they bring the bad stuff on themselves. Also by making it a self-inflicted role (most often because of a character's stupidity and short-sightedness) it also makes the torment more palatable.
If the entire cast is made up of Chew Toys of some kind or another, then you're probably watching a Sadist Show. Compare Hellistics (when unrelated events turn out to be connected with each other just to screw over the character) and Humiliation Conga.
No Real Life Examples, Please!. While life can certainly suck at times, nobody exists solely to suffer. Also, while someone’s suffering may be funny in fiction, that’s obviously not the case for Real Life, thus, there are no examples to be found.