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.
Shipbreaker Kraken
If you lose control of Shipbreaker Kraken between when its last ability triggers and when that ability resolves, the target creatures will become tapped. However, they won't be affected by the other effect and will untap as normal during their controllers' untap steps.
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.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Svetlin Velinov
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
