In addition to the already-mentioned Chasm City... Into the Sea of Stars by William R. Forstchen comes to mind. Generational ships take off from a dying Earth.

In addition to the already-mentioned Chasm City... Into the Sea of Stars by William R. Forstchen comes to mind. Generational ships take off from a dying Earth. The Earth recovers and faster-than-light technology is eventually developed. The FTL ships are tasked with tracking down the generational ships.