I think in SFC1 the game doesn't let you trade in your single ship if you don't have enough prestige to buy another ship "on the market," but I haven't played in a while.
Even you don't have any money in bank, if you can buy at least one ship in the shipyard after you sell the ship, you can still trade in it. In my experience, there always is a ship you can buy after selling the only ship. But it doesn't worth doing, since the current ship is always more powerful than what you can buy if you trade it when no money in the bank.
Using the following pic for example, you can still trade in your F5. But you can only buy a E4 after that, so it's not worthy.