The money came from a home that was paid for - Stacy's home - and half of that unencumbered asset was hers. Now, Drew essentially took the equity out - again, half of which was Stacy's - and gave it to his son. Therefore, since Drew still has the asset (the house) and it can be sold to satisfy the loan, half of the money is Stacy's.
So, why would Stacy's family want it? Drew still has the asset (the house) and can sell it to satisfy the loan obligation.
The reason Drew did that, was to assure the safety of that quarter-million dollars. If someone took the house (to satisfy a judgment), it would be all equity. If they take the house now, they have to first satisfy the loan obligation, what's left would be a pittance. Drew still has his money, let someone else worry about the loan payment. It was done to protect the equity and half of that equity is Stacy's.