It sounds like this stake was for one single $300 buyin. "Stakeback", or whatever you want to call it, really only applies if you plan on staking the guy in multiple sessions/tournaments.

If you just agreed to stake him in this one time, then you aren't owned anything. You can't really have a "stakeback" on a one time deal if he goes broke.

If you agreed to stake him over a longer term (ie this $225, then more on other occasions) and said that before he pockets his 50% of the winnings he has to pay his stakes back, then sure, he "owes" you. But you also must put up more stakes for him.

Cliff notes: Don't stake people who suck at poker and/or without a clear statement about the staking deal.