Private foundations can take the form of either a non-profit corporation or a trust. Both forms are governed by both state and federal law. Most private foundations can continue forever.
Upon dissolution, the organization's remaining assets must be distributed for one or more tax exempt purposes. Typically it involves giving the remaining assets to another non-profit organization.
Thanks to Nancy M. Bonniwell for sharing this information as part of the State Bar of Wisconsin's Annual Estate Planning Update - December 2011. Remember, a blog is not a substitute for legal advice.