dnd 5e – What happens when a creature clinging to a surface through the Spider Climb spell goes prone?

The Spider Climb spell does the following:

Until the spell ends, one willing creature you touch gains the ability to move up, down, and across vertical surfaces and upside down along ceilings, while leaving its hands free.

If the creature goes prone while under the effect of Spider Climb, do they fall off the surface or do they hang on to it?