Because the Browns' season is over, they likely can sign him to their extended offseason roster via a reserve/future contract.
Supposedly those contracts can only be offered to players who weren't on an active roster "when the season concluded," which could either mean (a) the season is over and if Clayton is cut in the postseason, he's still considered "under contract," or (b) if Clayton is cut by a team whose season is on-going, he is now not under contract at the conclusion of the season and can be signed to an offseason roster. I think the latter interpretation is more likely, for myriad reasons.