In Magic the Gathering, does an opponent keep their card if...?

When you cast a spell, you choose the targets. All targets must be legal at this time, or the casting is illegal, and the game is rolled back to before the spell is cast.

When the spell resolves, targets are re-checked for legality. If all targets are illegal at this point, the spell is countered as a state-based effect.

Their spell is countered by game rules, and ends up in the graveyard. From the rulebook, cause you wanted a source:

413.2a If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s moved out of the zone it was in when it was targeted is illegal. Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed or an effect may have changed the text of the spell. If the source of an ability has left the zone it was in, its last known information is used during this process to determine its characteristics. The spell or ability is countered if all its targets, for every instance of the word “target,” are now illegal. If the spell or ability is not countered, it will resolve normally, affecting only the targets that are still legal. If a target is illegal, the spell or ability can’t perform any actions on it or make the target perform any actions.