Let's say I bring out Steve Clarney (F23; While Steve Clarney is committed to a story all characters lose all Toughness.)

When I attach Steve to a story, any character with Toughness that also has a wound will die. But if such a character has an Action, could they activate the action as a parting shot.

I'm told that in Magic, for example, a card in the process of being eliminated has a chance to perform actions as a parting shot. The rules in CoCLCG aren't clear on this.

No. Actions take place at very specific timing intervals, and characters on the way out don't get a chance to do them. Breaking down the basic action types:

Action: Can only happen at specific timing intervals (noted by white boxes in the manual's timing chart).

Response: Whenever the conditions it states are met and it's a "white box" timing step, you can choose to activate a response (although it's after something finishes resolving, so you can't really "interrupt" anything with it, generally).

Disrupt: Actually interrupts things, this is the only action type that happen in the middle of things resolving, or stop something from happening (for example, a number of cards have disrupts "Disrupt: Pay 1 / exhaust to prevent a wound to this character" that you can use before a character would die from a wound).

Forced Response: You have to do these whether you want to or not, when the conditions are met, but like a disrupt, they can happen at any time.

In the Story Phase, for example, you have opportunities for normal actions before and after stories resolve, but not during - all three stories have to fully resolve first, before you can use anything but disrupts or forced responses.

Regarding your original question more clearly, now: once a character is about to die, say from a wound aimed at them by an event, you're in the middle of resolving something and thus couldn't do anything but a Disrupt. Hence why characters can't do actions "on their way out".

Thanks. Sometimes it's more confusing to play other games