Example: Felidar Sovereign reads, “At the beginning of your upkeep, if you have 40 or more life, you win the game.” Its controller’s life total is checked as that player’s upkeep begins. If that player has 39 or less life, the ability doesn’t trigger at all. If that player has 40 or more life, the ability triggers and goes on the stack. As the ability resolves, that player’s life total is checked again. If that player has 39 or less life at this time, the ability is removed from the stack and has no effect. If that player has 40 or more life at this time, the ability resolves and that player wins the game.
701.4a To cast a spell is to take it from the zone it’s in (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. A player may cast a spell if they have priority. See rule 601, “Casting Spells.”
113.7a Once activated or triggered, an ability exists on the stack independently of its source. Destruction or removal of the source after that time won’t affect the ability.