The stores include Bon-Ton, Bergner's, Boston Store, Carson's, Elder-Beerman, Herberger's and Younkers.
Bon-Ton has been hit hard by competition from big box and online retailers.
At least one other Zamias property - Indiana Mall in Indiana, Pa. - also leases to a Bon-Ton store, according to the mall's website.
Bon-Ton Stores is closing all its locations, including 18 Younkers stores across Iowa; four are in the metro.
Rice Lake has had a Herberger's store since 1945, when it opened on the east side of Main Street, north of Messenger Street.
The Bay City Town Center had been gaining momentum with the opening of a new Younkers Home store in November 2016 after Target and Sears left the shopping center in 2015. It previously operated stores at Destiny USA in Syracuse, Great Northern Mall in Clay and ShoppingTown Mall in DeWitt.
Employees at the Olean store declined to comment Thursday, recommending questions be sent to a corporate official.
The going out of business sale at the Carson's store in the Cross County Mall is scheduled to start on Friday, April 20. J.C. Penney announced last February it was closing the Holland location and ended up closing for good on July 31. After 160 years in business, all stores will be closed no later than August 31st. "I think people are nervous", said Purush Papatla, marketing professor and interim Associate Dean of Academic Affairs at the University of Wisconsin-Milwaukee.