What happens to a suspended card if the player who owns it loses the game?

When a player loses the game, all permanents they own are removed from the game, and all spells and abilities they control on the stack cease to exist. However, cards in exile are a special case — they remain in the exile zone even after their owner loses (CR 800.4a).

A suspended card is a card in the exile zone with time counters on it, waiting to be cast (CR 702.61). The suspend mechanic uses a triggered ability that fires at the beginning of the owner's upkeep to remove a time counter, and another trigger when the last counter is removed to cast the spell. If the card's owner has lost the game, those triggered abilities can no longer trigger because that player no longer takes turns or has an upkeep (CR 800.4).

The result is that the suspended card simply sits in exile indefinitely. It will never be cast because no upkeep trigger will ever fire for the player who owned it. It does not go to a graveyard or anywhere else — it just stays in exile, stranded there for the rest of the game (CR 800.4a).

Example: Your opponent suspends a Ancestral Vision with 3 time counters. Before those counters are removed, they lose the game. The Ancestral Vision stays in exile with its remaining counters but can never be cast — the upkeep trigger that would remove counters no longer has an owner to trigger for.

Note: In multiplayer games, if another effect somehow transferred control of the suspend trigger or the card itself before the player lost, edge cases could arise, but under normal circumstances the card is permanently stranded in exile (CR 702.61b, 800.4a).