It was a real hassle on the cruise ship when people jumped ship in the USA, would often result in all shore leave banned for the subsequent US Ports.... Grrr...
However the US Border Protection usually got the guys. Most of the Filipinos who jumped ship had family in the USA, but had forgotten that 3 or 4 years previously they'd completed a visa application (C1-D) to allow them to enter the US as a seafarer, one of the questions of which was do you have family in the USA and please give their addresses. The Border Officers just looked in their files and would head straight to those addresses and usually found the offender!