Does a creature become a 0/0 and die immediately if it loses all +1/+1 counters that were keeping it alive?

When a creature loses +1/+1 counters, its power and toughness are recalculated immediately. If the creature's base toughness is 0 (for example, a 0/0 creature) and it had +1/+1 counters keeping its toughness above 0, removing those counters causes its toughness to become 0. State-based actions then apply and the creature is put into the graveyard. This is governed by CR 704.5f, which states that a creature with toughness 0 or less is put into its owner's graveyard.

State-based actions are checked continuously by the game whenever a player would receive priority (CR 704.3). They require no player action to trigger — the moment the creature's toughness hits 0 or less, the game automatically destroys it before anyone can respond.

It is important to note that this is NOT the same as lethal damage. A creature with 0 toughness dies via state-based action (CR 704.5f), while a creature with damage equal to or greater than its toughness dies via a different state-based action (CR 704.5g). Both result in the creature dying, but the mechanism differs.

Concrete example: You control a Hex Parasite (a 1/1 creature) and activate its ability to remove all three +1/+1 counters from your opponent's Epochrasite (which entered as a 0/0 with three counters, making it a 3/3). Once the counters are removed, Epochrasite becomes a 0/0. Before anyone can respond or take action, state-based actions are checked, toughness is 0, and Epochrasite is immediately put into the graveyard.

Note that if the creature has a base toughness greater than 0, losing counters may reduce it but not kill it unless the final toughness reaches 0 or less. For instance, a 2/2 with two +1/+1 counters losing both counters becomes a 2/2 — it survives fine.