Is it permissible to delay or default on payments to the former partner after the restaurant's loss, knowing that half of the agreed-upon amount was paid before the restaurant's closure?

If you have properly purchased your partner's share, its price becomes a debt that must be paid at the agreed-upon time. Delay is not permissible unless you are unable to pay. In that case, the creditor must grant you a respite until you find ease, as Allah Almighty says: "And if there is one in [financial] difficulty, then [let there be] a delay until [a time of] ease."