Scenario.

My opponent uses Chomin's ability. In response to him paying the cost (stunning his character), I flip Mutant of the Year - meaning he can't target me. Does this now mean that he must target himself with the "burn", as he is the only legally targetable player?

No.

The target is announced when you use the ability and stun the character. Flipping Mutant before the effect resolves simply means that the burn effect fizzles as the target is no longer legal. You can't retarget at this stage.

If it's done in response then it just fizzles, as there was a legal target when the effect was generated.

OK, cool, but if my opponent has a brain fart and plays it - let's say - the turn after I flipped MOTY, he would be burning himself?

He couldn't accidentally burn himself, as he has to announce the target when declaring he is using the ability and paying the cost. He could try to use it targeting you but it would be an illegal play and the use of the ability would be cancelled.

He could choose to target himself if he was desparate to stun one of his characters *cough* Xallarap *cough* or was playing Shadowpact for example, but he couldn't accidentally do it.

Once he puts the effect on the chain he has to announce which character he will stun to pay the cost of the effect, then he has to choose a target for the effect. He can't choose you as a legal target for the effect. Does he have to then choose himself as a target... hmmm, I'm not sure. Can't find anything on whether he can option out of choosing himself as a target.

OK. Thanks for clearing that up. Cheers.

His chosen target is illegal so you rewind the game state to before he tried to play the effect.

The rules don't really specify that if you have a legal target for the effect you are forced to choose that target, but they also don't indicate that you can option out of choosing it. I think though that rewinding is the right way to go.

You choose targets before you pay costs. That distinction is important.

If he did pay the cost not realizing you were an illegal target it could be questionable along with Child of Valeria which forces the stun if you control Doom (you must choose a target even if its yours).

This is true. I'm mixing up the steps because there is this section of 505.1b that comes before choosing targets.

In hindsight I don't think that the cost associated with Chomin's effect would qualify. His text reads.

"Stun a character you control other than Chomin >>> Target player loses endurance equal to the cost of the character you stunned. Use this power only once per turn."

In this case I don't think the cost would be determined until after targets are chosen. Though, it still doesn't really answer my question of whether Chomin's controller has to choose a target, since he is a legitimate target, or whether he can choose not to find a target.

Child Named Valeria was errata'd long ago to become a "choose one or both" card, like Marvel's First Family, to avoid such problems.

ah thank you kindly for the update. Note to self reread errata page before designing next golden age deck.

Pretty sure they changed A Child Named Valeria because the wording forced you to have an exhausted character to target for the effect to resolve.