MACON, Ga.—Many struggling shopping malls are trying to find salvation by going small—in their purchasers, sales prices and, in some cases, size.

As the nation's largest mall owners sell off or give up their most-troubled properties—dogged by deteriorating neighborhoods, newer rivals and online sales—smaller real-estate companies are snapping them up at discount prices and trying to find ways to pull them out their death spirals. Sometimes, that involves demolition.

It...