I doubt you will find a Hyatt give away
If you check Red Week, Hyatt is one of the few timeshare companies that actually still sells. Granted they are much cheaper then they were a few years ago, but my sister in law is looking for a Hyatt week and they are still selling.
Plus I would be shocked if Hyatt would let any of their units go for "free" - they all have ROFR. All Hyatt properties have weeks available for sale, everytime we go to a Hyatt timeshare (we are owners) they try to sell us another week.
I know I am bumping up your post - but you may want to check Red Week and try a low ball offer on a lower priced week in Arizona or Texas. All the Florida properites are still selling, Texas or Arizona are the places where I am seeing anything that I would consider a great buy. There is always Puerto Rico, but I would not take that - even for free!