There are many complicated halachos about closing down and selling a shul building. Particularly if it was built with funds solicited from the public. In the 1970s when many neighborhoods were deteriorating and many shuls were closing down it was a major contentious issue with many Diney Torah and L’havdil law suits.
There are too many factors involved to discuss it here.
I know of some shuls that made a deed restriction that if the shul ever closes down and the building is sold then some external organization like the Agudah or the OU will (1)decide where to distribute the money but (2)can not distribute the money to themselves in order to avoid a conflict of interest when the shuld gets sold