In newer and/or smaller tanks, clams like that should be fed. Be aware it may starve regardless, and be ready to do a lot of water changes if it does. Bivalves rot fast and turn into the world's most disgusting soup inside the shell. If it dies, you may be able to pull it off the rock, as the foot will start to degrade. On the chance that happens, I would pull the whole thing out, dump out the grossness inside (OUTSIDE the tank, hold the shell shut until it's out), rinse it, and then put the shell back in, as there's lots of stuff living on it. Hopefully it lives, but it may already be in poor health depending on how long it's been without much food.
It looks like maybe a turkey wing clam. Too bad it doesn't look like anything photosynthetic, or it could get some energy that way.