Are we including:

FPSes with items where taking cover behind them will cause them to fall apart? Just FPSes with destructible walls and/or a cover mechanic? Or no FPSes at all?

Also, what do we call destructible cover. Do cars that explode count?

Affirmative to all of the above. At least that's what I'd say.

If it's something you can take cover behind that can be withered away at or destroyed then it's destructible cover.

I'm not sure about exploding cars though, since that is just a destroyable object, they usually don't move at all. You can come back to it after it explodes and still use it as cover so....blah I'm confused

Well, in GRAW I think I remember not being able to use a tank as cover once it blew up.

in the case that u can take cover behind a car, and its explodable, its destructable cover.

@SavageGuy

I literally laughed out loud at the sight of your post.  Hilarious.