No. If a generic version of a chemical molecule is not developed by anyone, even after expiration of the patent on an innovative medicinal product, the innovative product would still remain the only approved product available. Sometimes a generic version is approved and available in a specific country or countries, whilst in other countries the innovative product remains the only product on the market.
However, with the growing emphasis on generics, it's rare that a generic version or more than one generic version of a chemical molecule is not developed around about the time that its innovative counterpart comes "off patent". The reason for not doing so may be, for example, a complex manufacturing process of a drug designed for a limited use, where the cost of developing and selling a generic version of the product would not be viable.