Short answer: a minor part of it (about 1/4) was captured by Croatian forces in 1991 and formed Croatian navy. Most of the ships were withdrawn to Montenegro after direct Yugoslav involvement in Croatia ceased in 1992, where they were included in the FRY Navy and, after 2006, Montenegrin Navy. Most of ex-Yugoslav ships are out of service by now.

Long answer: Yugoslav Navy spent the first few months of war in 1991 mostly out of combat operations (except for a failed landing near Italian border during the intervention in Slovenia). The war for it started in September, when Croatian forces attempted to seize Yugoslav barracks scattered around Croatia, together with any hardware in those barracks. This "Battle of the barracks" included seizing of several Yugoslav naval vessels, mostly in Šibenik, in the local naval base and naval shipyard, but some also in Ploče and Vela Luka, plus unfinished vessels in shipyards. Most of those vessels were in various states of disrepair and couldn't be used for naval operations anyway.

At the same time, a significant part of Yugoslav coastal artillery was seized by Croatians. The naval infantry battalion was a multinational unit and quickly fell apart.

In response to Croatian sieges and attacks on the barracks, Yugoslav forces launched an offensive in Croatia. Naval part of this offensive included a blockade of all Croatian ports, and they kept it up intermittently until November. Mostly it was meant to prevent Croatia from importing arms by sea, but on occasions Yugoslav ships have also shelled cities (which led to a tragically ridiculous situation of frigate Split shelling the city of Split). On 14th and 15th November, Croatian coastal artillery attacked Yugoslav ships blockading Split and damaged two of them: both were captured but one was a total loss. After that clash, blockade was mostly lifted (except for Dubrovnik). After the Sarajevo armistice, all ships retreated to their bases in Montenegro, and became the part of the Navy of FRY. After Montenegro became independent in 2006, all remaining ships became part of the Montenegrin Navy. Most were struck during the 2000's.