The founder may probably not sell without board approval, but it is a matter of state law.  The sale of substantially all of the assets of a nonprofit corporation is normally a decision that has to be approved by the members, if there are members of the corporation with voting rights.  If the founder is the sole member of the corporation, he/she may be able to approve the sale without a vote of the board, but I doubt that would be universally true.  If there are no members, obviously the board would have to approve.  If there are members other than the founder, the other members may or not be able to act without the board voting. It clearly makes sense to get board approval, but it may not be legally required.  You should check the membership status of the founder and the state law to see whose approval is required.

A 501(c)(3) may be sold at a “profit,” usually by selling all of the assets to another entity.  In many states, the state attorney general will want to review any proposed sale of substantially all of the assets to assure that the price is fair, that there is no inappropriate private benefit, and that the net remaining assets continue to be used for charitable purposes.  Many 501(c)(3) organizations that are sold, particularly charitable hospitals, continue as grantmaking foundations.  (See Ready Reference Page:  “Conversion Foundations Face Key Issues Early”)  Others dissolve and distribute their net remaining assets, as required by the IRS, for other charitable purposes.