Who maintained ships laid up in ordinary?

Did naval crews stay aboard ships when they were laid up in ordinary?

No. The commissioned crew left, and the Navy Board took responsibility for the ship and the personnel maintaining it.

A ship placed in ordinary no longer retained its commissioned crew. Responsibility passed to the Navy Board, including authority over the people maintaining the vessel. The board formally belonged within naval administration but had enough independence to resist Admiralty direction. A maintained hull therefore did not imply that the same crew or chain of command continued from active service.