In most jurisdictions, the owner(s) of the marina, or storage facility, have a prescribed time period of non-payment before they can take legal action. This varies from state to state, but once that prescribed time frame has been met, then the next step becomes quite involved.
In most instances, a registered letter must be sent to the registered owner(s) of the vessel that essentially tells them they must pay the storage fees or the boat will be confiscated and sold at auction.
Usually, upon receipt of the letter the registered owner(s) have 90 days to respond. If no response is received by the deadline date, the storage facility must then petition the state department of Natural Resources Boating Administration to place a storage lien on the vessel, which takes approximately 60 days to obtain.
After obtaining the storage lien, the facility must then advertise their intent to auction the vessel in at least two newspapers published in the area where they previous owners reside. This must be published at least two months prior to the auction. If they still fail to respond and pay the current storage fees, the auction can take place at the advertised time.
The above is a broad synopsis based upon information I obtained from the Maryland Department of Natural Resources Boating Administration, Florida Department of Fish & Game, State of California, and City of New York while researching a magazine article I had published more than five years ago.