Will a creature that is a copy of Skullbriar, the Walking Grave retain it's counters as it moves to another zone? For instance, if a Clone enters the battlefield as a copy of Skullbriar, later gains counters, is sent to the graveyard, and then enters the battlefield from the graveyard as a different creature, will it still have its counters? (Is this answer different if the Clone, upon re-entering the battlefield, becomes a copy of Skullbriar again?)
Similar but different question: if Lazav, Dimir Mastermind becomes a copy of Skullbriar, gains counters, and then is sent to the command zone, will it retain the counters? If Lazav is cast as a commander again, will it retain those counters as it enters the battlefield the second time?