Hello. The answer to this may be controlled somewhat by the local jurisdiction, but in general if the fees are not paid then the slipholder no longer has the right to use the slip. The marina could move the boat, including hauling it out if they desire. They could also refuse to allow the boat back in the slip if it leaves. Generally there is a written contract that may spell out terms, and in any case the non-payment would be enforceable in court - probably Small Claims in most jurisdictions. Finally, a lien could be placed against the boat for the non-payment if the amount justifies it.
Here is another idea from another one of our experts here. Note that I would not necessarily recommend this, but it could be used if you really get into a bind:
I would untie it from the sip as it [the slip/mooring/pilings, etc] belongs to you and is private property, then once adrift claim salvage rights, lodge the salvage with the Coast Guard, and let them know where the boat has been salvaged to, ie your marina. You will then be entitled to charge for the cost of salvaging the vessel and storage which I would imagine would amount to the total owed.
Marine Mechanic
USCG Licensed Captain, 20+ Years Boating, Fishing, Maintenance and Repair Experience