Keepsake Gorgon

Deathtouch
{5}{B}{B}: Monstrosity 1. (If this creature isn't monstrous, put a +1/+1 counter on it and it becomes monstrous.)
When Keepsake Gorgon becomes monstrous, destroy target non-Gorgon creature an opponent controls.

Pioneer Masters

Conspiracy: Take the Crown

Theros

An ability that triggers when a creature becomes monstrous won't trigger if that creature isn't on the battlefield when its monstrosity ability resolves.

Monstrous isn't an ability that a creature has. It's just something true about that creature. If the creature stops being a creature or loses its abilities, it will continue to be monstrous.

Once a creature becomes monstrous, it can't become monstrous again. If the creature is already monstrous when the monstrosity ability resolves, nothing happens.