Is it permissible for the seller to increase the agreed-upon price in exchange for a new extension of the payment period, in the event that the buyer, who is able to pay, defaults, or the buyer is unable to pay and wishes to extend the payment period?

Selling on credit is permissible. It is also permissible to agree on one price for a cash sale and another price for a credit sale, but it is necessary to specify which of the two prices the buyer chooses to complete the contract. However, if the contract is concluded before specifying the price, it is not permissible due to the ambiguity of the price, based on the saying of the Prophet (peace be upon him): "The Messenger of Allah (peace be upon him) forbade two sales in one sale." If the two parties agree on the deferred price, it is not permissible to increase the price in exchange for extending the term; because that is usury (riba), which is forbidden. The seller should grant respite to the one in hardship or sue the procrastinator to take his right without an increase.