Well currently we have them on the list with the other FCs just like the Capitol character FCs. As far as claiming goes I believe it is just like the regular face claim rules. The claim belongs to the person who has it originally. If that person wants to allow someone to use their claim they could share it as long as both people are ok with this. Or so I believe...I guess that is, really up to the original claim holder. But yes, all claimesd playbys who are not dead characters are on the main list.
**Edit: Also wanted to clarify that since adult characters (any previous reaping eligible character you had in the district, non victor 18+ year old, etc) are RPable the claim still counts as a characters claim. If you decide to get rid of the character and release the claim you may. But you do not have to since we have mandatory aging now and there is more RP opportunities for characters over reaping age.