[@DisguisedDemon] Course they do that. You just start a new Interest Check, don't even have to mention there was another same RP before that died, and start accepting new people as you go. You either leave this RP thread as it is, or you put something in the IC and OOC saying that the thread has been restarted with new people and that anyone interested goes to the Interest Check/new RP thread (make sure to put a link and write the note easily visable onto the first IC and OOC page! (edit it in) and maybe even the last one (for old people to see it too, because only new people usually land directly on the first page you know))

That's what I'd do at least. 
Step 1) create a new individual Interest Check and/or RP thread
Step 2) put the link on the first and last page of the old RP thread, easily visable and with the note to drop by if interested
Step 3) just restart like you did before
Step 4) HAVE FUUUUUN

LoL you that's what I'd do.