In PSIV Chaz and company explore the crash site of one of the ships that fled Parma*
In these ruins they learn the sad fate of the fleeing ships, and briefly ponder if any are still searching for a home.
PSIV was always called sequel to PSII. PSIII actually occurs after or during PSIV*
PSIII's only mention in PSIV is this brief dialog.
On the plus side, there appears to be descent chance that PSV (aka PS Online)
may run concurrently to PSIII. It's too early to tell because only general plot details have been released.
Jump over to the download
page to get a PSIV save state of this sighting.