The UPL Remnants will survive by hiding underground and the Protoss will save them.
Just like in the original Legacy of the Confederation, the last fragments of the UPL will probably continue resisting the Zerg occupation underground, and possibly, a more benevolent group of Protoss different from the ones in the prologue (the latter presumably having been the ones responsible for luring the Zerg to Sol) will arrive to defeat Cerebrate Slohr and free the Terrans from the Zerg. Though how the Protoss rescuers would be drawn to Sol remains to be seen, as unlike in LotC, the attempt to send a message via SETI fails in the UED:FL timeline. The UED will be split between those who want to control and those who want to exterminate the Zerg
In LotC, the Confederation (not to be confused with Koprulu's Terran Confederacy, which had already been dissolved and succeeded by the Dominion at that point) that formed after Earth was freed from the Zerg sought to exterminate the latter out of vengeance, but eventually a group of Cerebrates on Char not under Kerrigan's control offered to negotiate their surrender to the UPL, which their president was considering, but the admiral disagreed and staged a mutiny to take control of the UPL Koprulu fleet to continue the extermination campaign. It is possible that in the UED:FL timeline, there will be a similar split between the forces under DuGalle and/or Stukov who wish to enslave the Zerg broods just like in the canon events of Brood War, and those under a renegade commander (possibly named Ra'chek as a nod to LotC?) who wishes to continue eradicating the Zerg.