Betye Saar's Ancestral Spirit Chair is a great example of this.
Purchased with the proceeds from the sale of a work donated by Mr. and Mrs. Alexander Rittmaster (Sylvian Goodkind, class of 1937) in 1958 and with funds realized from the sale of a work donated by Adeline Flint Wing, class of 1898, and Caroline Roberta Wing, class of 1896, in 1961, 1992:42a-c
When a museum tries to break this rule, it can get in serious trouble with the Association of Art Museum Directors (AAMD). Consequences are that the museum cannot borrow works from other museums, including traveling exhibitions. When you break the rules, you don't get to play.
See the (Example) The Kemper Museum of Art at the University of Washington, St. Louis for another example of the Purposeful Use of Funds.