What happens when a creature with undying dies with a +1/+1 counter on it?

Undying reads: 'When this creature dies, if it had no +1/+1 counters on it, return it to the battlefield under its owner's control with a +1/+1 counter on it.' The critical condition is that the creature must have had no +1/+1 counters at the moment it died (moved to the graveyard).

When the game checks whether Undying's trigger condition is met, it uses the 'last known information' rule (CR 702.93a, CR 603.6d) — it looks at the creature's state just before it left the battlefield. If even one +1/+1 counter was on it at that moment, the Undying ability does not trigger at all, and the creature simply stays in the graveyard.

This is a common interaction with Undying creatures that have already returned from the graveyard once (since they come back with a +1/+1 counter), or with creatures that received +1/+1 counters from other sources like pump spells or proliferate effects.

Example: You control a Geralf's Messenger that previously died and returned via Undying (so it has a +1/+1 counter on it). Your opponent destroys it with a removal spell. Because it had a +1/+1 counter when it died, Undying does not trigger, and Geralf's Messenger stays in the graveyard.

If you want to 'reset' an Undying creature so it can come back again, you can remove its +1/+1 counter before it dies — for example, using a spell or ability that removes counters — so it dies with zero +1/+1 counters and Undying can trigger again.