The term "reverse piercing" the corporate veil refers to a doctrine whereby courts disregard the corporation as an entity separate from one of its shareholders. In this sense, reverse piercing is similar to the more familiar doctrine of piercing the corporate veil. The difference is that in regular, "forward" veil piercing, a creditor of the corporation is typically attempting to hold a shareholder personally liable for debts of the corporation, whereas in reverse piercing a creditor of the shareholder is typically trying to hold the corporation liable for debts of the shareholder.
One might wonder why reverse piercing is necessary. The creditor of a shareholder can already indirectly reach the corporation's assets because the creditor can reach the shareholder's stock, which could be sold to pay the claim. The answer is complex because reverse piercing arises in more vaired contexts than traditional veil piercing. Under some statutes it might be advantageous to treat the assets of a corporation as assets of the shareholder. In other contexts, it might simply be easier to bypass the two-step process of proceeding against the stock and then dissolving the corporation or selling the stock.
In any case, reverse piercing is controversial. The doctrine is problematic when the relevant corporation has multiple shareholders, and even when there is only one shareholder it can give creditors of a shareholder an advantage they would not normally have relative to creditors of the corporation. As a result, reverse piercing is less universally recognized than traditional veil piercing, not having been accepted in all state courts.