It’s a joke grenade which instead of exploding just sprouts out some harmless gas. Probably all of the grenades they gave to the people in the bank were like that. I figure the Joker probably wouldn’t want to get fragged during a routine bank robbery just because some scared-to-all-hell civilian’s hand slipped and a live grenade went off.
Fichtner’s character did get shot, though, so he could’ve died from his wounds, or like Linty Fresh suggested the mob might’ve whacked him as a penalty for his failure. It doesn’t really matter in the grand scheme of things as he is a minor, nameless character.