Is it permissible, in Sharia, to stipulate that my aunt receive a house from the municipality for the sale to be completed, and what should be done if this condition is not met?

If the agreement between the seller and the buyer is that the contract is not concluded until the aunt acquires a house, then this is merely a promise to buy and sell, and the sale has not yet taken place because it is not permissible to make it conditional. The amount paid as part of the price is a trust. If the buyer authorizes the seller to dispose of the money, it is a loan, and it is permissible to retract the promise.

Even if the sale were concluded and the seller made an exception for the benefit of dwelling with this condition, the contract would be void due to the uncertainty of the duration of the exception. The Prophet (peace be upon him) forbade selling with an exception unless it is known. This exception is unknown due to the unspecified term, and those who permit the exception of benefit stipulate that the duration must be known. Therefore, there is no disagreement regarding the invalidity of stipulating an unknown benefit.