I believe the moon must be orbiting faster than the planet’s spin for that to happen (both the moving closer and the spin acceleration).
And, looking it up, that is indeed the case for Phobos, the larger of Mars’ moons, and it is getting closer and will eventually either break up or crash into the planet, while also applying a force that increases Mars’ spin rate.
Deimos is orbiting slower, so won’t share that fate, though maybe it’s orbital radius will increase enough for it to escape the Martian system, though I doubt it since it’s already close to the Martian day.