What is my immigration status if I do not return to the US ship after leave is up?

Assuming you are on a D-1 crewman visa and do not return when the I-94 card expires then you are an overstay. This is not a good idea as there are many special restrictions on crewmen (even if you were to marry a U.S. citizen). If you want to remain in another classification best to go home and re-apply for the new classification. The consulate will see you complied with the visa as required and this will be in your favor for future applications.

A C1/D2 crew member must return to their ship. They cannot adjust status, nor seek relief for the most part. A person who overstays a C1/D2 can be deported They usually have no right to adjust status even if they marry a U.S. Citizen. It is best to consider consular processing and leave with the ship. Should negotiation be needed, you may need an experienced Filipino licensed attorney who practices Filipino maritime or armed forces law. There has only been one exception in the history of immigration law. However, if you were not petitioned directly or indirectly for an immigration visa by January 14, 1998, then you cannot do much. I strongly recommend an appointment or teleconference to consider all of your options.