If the targeted creature loses all its -1/-1 counters by the time the ability resolves, the ability won’t resolve because its only target is illegal. The creature won’t be destroyed.

You can’t target a creature unless it already has a -1/-1 counter on it as your upkeep begins. Putting a -1/-1 counter on a creature during your upkeep won’t let Crumbling Ashes destroy it that turn.

This ability is mandatory. If you’re the only player who controls a creature with a -1/-1 counter on it as your upkeep begins, you must target one of your own creatures.