Is what the heirs received from selling the apartment to the second buyer—after the broker brought another buyer at a lower price following his dispute with the first buyer over the latter's refusal to pay the commission—lawful or unlawful?

The sale is valid, and the price is permissible for the sellers. The sale is not considered bidding over another's bid (sawm ala sawm al-ghayr) that is prohibited, because the prohibition applies when the seller explicitly expresses satisfaction with the sale. Ibn Qudamah mentioned in Al-Mughni the categories of bidding over a bid, which are: 1. When the seller explicitly expresses satisfaction with the sale: In this case, bidding over the bid of that particular buyer is forbidden, and this is what the prohibition addresses. 2. When the seller shows signs indicating dissatisfaction: Bidding is not forbidden in this case, as the sale is open to whoever offers more. 3. When there are no signs from the seller indicating either satisfaction or dissatisfaction: Bidding is also not forbidden, nor is increasing the offer. 4. When the seller shows signs indicating satisfaction without explicit declaration: Haggling is not forbidden. The general principle is the permissibility of bidding and proposing (ukhtubah), so what is forbidden is that in which explicit satisfaction is found, and everything else remains under the original ruling.

The sale is valid according to the majority of scholars, even if it is assumed that what occurred was an instance of bidding over another's prohibited bid.