The unique problem here is that while many of these are designed to run nicely from USB drive, I don't get the impression that many will let you remove the USB drive after boot.
FatDog talks about running from a RAM layer, which is cool. But I believe even this is still a RW layer atop the underlying root which needs to remain mounted.
Nope, puppy (all variants), fatdog, and porteus (all variants, including porteux & nemesis - which is arch based) can all boot in a mode where you can unplug/unmount the storage device from which it booted.
The unique problem here is that while many of these are designed to run nicely from USB drive, I don't get the impression that many will let you remove the USB drive after boot.
FatDog talks about running from a RAM layer, which is cool. But I believe even this is still a RW layer atop the underlying root which needs to remain mounted.