"He received a final payout on 12/31/20 which was equal to 1/3 of the cash on hand."

Who guided them on this? Because you describe: He got his share of funds on hand.

That means there is Nothing else of value that would be his? You cannot buy him Out of the partnership with his own Equity (share of funds on hand).

However, the other two partners can buy him out, personally. That would be after taking into consider the Value of his third, of course.