Longtime lurker but first time poster. Usually I see the answers converge on rightness after a few posts, but it seemed like you could use some help here.
The answer to the OP’s question depends on the state of incorporation. At least in Delaware, a corporation can’t directly do what the OP proposes. I’m guessing it’s similar everywhere else since Delaware is effectively a model for most other states’ corporation laws.
A typical corporation that you are familiar with is a “stock corporation,” i.e., one whose ownership is evidenced by issuing stock to equity owners. There is such a thing as a “nonstock corporation,” which has ownership that is not evidenced by stock (most commonly, these are non-profit organizations).
The OP is effectively asking, can the owner of 100% of the shares of a stock corporation convert it to a nonstock corporation with no equity owners by selling or giving his or her stock corporation shares back to the corporation? The answer is no under Delaware law. This is true even if the transaction wasn’t fraudulent in any way, even if the sole shareholder really wanted to do it, and even if the corporation wouldn’t be insolvent or bankrupt after the transaction. Those are all separate issues.
When a corporation forms, it must declare on its articles of incorporation (filed with the state) whether it is a stock corporation or a nonstock corporation. The articles of incorporation actually define all the powers that the corporation has and will ever have. The corporation can’t do anything that its articles of incorporation won’t allow it to do. Importantly, the articles of incorporation define whether the corporation can act as a stock corporation (with one set of requirements for showing ownership and effecting control over the corporation) or a nonstock corporation (with an entirely different set of requirements for showing ownership and effecting control). See http://delcode.delaware.gov/title8/c001/sc01/index.shtml
The OP’s shareholder can’t convert the stock corporation to a nonstock corporation because the resulting corporation would be acting outside the powers given to it under state law and its articles of incorporation by attempting to operate as a nonstock corporation. (Acts outside a corporation’s powers are referred to as “ultra vires.”) A stock corporation’s articles of incorporation and bylaws govern the way that boards of directors are elected, dividends are distributed, corporate decisions are made, etc. There is no way for it to act legally under these provisions if it suddenly becomes a nonstock corporation.
The owner of 100% of the shares of a stock corporation could accomplish the goal of converting it to a nonstock corporation by other means. What he or she would do is establish a nonstock corporation with appropriate articles of incorporation, bylaws, and membership requirements under state law. Then he or she would give or sell all the shares in the stock corporation to the nonstock corporation. The nonstock corporation could then pay off the stock corporation’s creditors (if any), dissolve the corporation, and retain all the remaining assets that used to belong to stock corporation.