If by "unsupported" you mean "free", I think there was a 24 hour thing at White Rock Lake a couple of years ago.  It did ask for a contribution, but was otherwise rather freeform.  I didn't do it, as it sounded like Bedlam to me.
 
You are invited to check out The Texas Time Trials, starting next Thursday at Glen Rose.  The 24 hour starts Friday at 18:00.  All the races are timed to end some time on Saturday (unless someone does the early start on the 500 miler and goes really fast).  GHQ is in the little park next to the Sonic coming into Glen Rose on SH67.

By unsupported I mean no support crew required.
 
Thanks for the info.......

I've done plenty of these, actually I quite prefer them over crewed support ones.     As Bob mentioned, the texas time trial is a good one to consider here locally.  But beware  its not a skinny tire ride,  those roads are rough
 
Quote from reever on Sep 17^th, 2016, 8:00pm:

But rereading this thread, you don't want to do those I think. You're looking for loop based races where you don't need crew. Not exactly the same.