What if the combined armies of the USSR, PRC and North Korea completely take over all of Korea and install a completely communist government that lasts to this day as OTRL North Korea has?
Even Jeju-do Island? Highly unlikely, possibly along with Ulleundgdo, if the South Koreans have any help at all from the UN/US. True, there was a nasty, brutal, and terrible civil war/uprising still simmering with the island natives, but pretty well over and done with by that POD of 1950 (presumed).
If the South Korean mainland was lost, the plan was for the US to transport all remaining persons to "an island in the Pacific", which I guess to be Jeju Island.
Were that not possible, then Guam, Rennel, Christmas Island (Pacific, not Indian Ocean) or some other rock.
History can be incredibly consistent. Expect a more self reliant and bellicose communist Korea. At about three times the population, it has more reserves. Also, the US would be less likely to be interested, so not willing to fork over dough for non existant nuke concessions.