When a Sailor pays off a debt to the command (advance pay, overpayments, etc.) they say they have paid off a Dead Horse. The saying comes from a tradition of British sailors. British seamen, apt to be ashore and unemployed for considerable periods of time between voyages, generally preferred to live in boarding houses near the piers while waiting for sailing ships to take on crews.
During these periods of unrestricted liberty, many ran out of money, so innkeepers carried them on credit until they hired out for another voyage. When a seaman was booked on a ship, he was customarily advanced a month's wages, if needed, to pay off his boarding house debt. Then, while paying back the ship's master, he worked for nothing but "salt horse" the first several weeks aboard.
Salt horse was the staple diet of early sailors and it was not exactly tasty cuisine. Consisting of a low quality beef that had been heavily salted for preservation, the salt horse was tough to chew and even harder to digest. When the debt had been repaid, the salt horse was said to be dead and it was a time for great celebration among the crew. Usually, an effigy of a horse was constructed from odds and ends, set afire and then cast afloat to the cheers and hilarity of the ex-debtors.