When a company's shares get "delisted," they disappear from the exchange on which they had been trading. Sometimes they disappear completely, but other times they don't. Depending on the reason for the delisting, the shares may continue to trade -- although buying delisted stocks can carry considerably more risk than buying those still traded on an exchange.
Some companies delist by choice. If a company reorganizes through bankruptcy, a merger or some other process, it may cancel its stock, in which case the shares must be delisted. Those shares become worthless. New shares will be issued; owners of the old shares may receive new shares, or they may get nothing, depending on the reorganization. Other times, investors "take a company private" by buying up all the outstanding shares. In that case, the shares will be delisted because the stock is no longer held by the public. The shares may still exist; they're just consolidated in the ownership group.
Most delistings are involuntary: the company doesn't want to delist, but it has no choice because its shares no longer meet the exchange's standards for remaining listed. Those standards relate to the value or performance of the company and include a minimum share price, usually $1. If the price can't stay above that minimum, the delisting ax falls. The stock, however, remains valid. If you own a share, you own a piece of the company, and as long as the company has some measurable value, so should the stock.
Over the Counter
As long as the company remains in business, the stock can still trade -- and even if it goes out of business, the stock may still trade, if investors think there will be anything left over to distribute to shareholders after liquidation. But since it's no longer allowed on the exchange, it has to trade "over the counter," or OTC. That means shares are bought and sold directly from one investor to another over computer networks operated by stock dealers and brokers, rather than through an exchange acting as a central clearinghouse.
The Problem With OTC
Companies don't get delisted because they're in good shape. They get delisted because they're in serious trouble. The very fact that the company has been exiled to OTC land means that market interest in the company is somewhere between slim and none. The larger market just doesn't want the stock. Many investors, large and small, make it a policy never to own an unlisted stock, so the delisting drives the shares even lower, possibly into a death spiral that sends the company to bankruptcy court. Demand for active OTC stocks still exists -- some people are always willing to take a chance on a bargain -- but it's so small that a single large trade can often send the share price soaring or plummeting. That makes OTC stocks highly volatile -- and vulnerable to manipulation. Trading in OTC stocks is not for the faint of heart.