For most part, a stock broker remains profitable and continues his operations. However, if it goes out of business for some reason, it shall transfer its investments to some other firm. It is his responsibility to safeguard your investment at all costs. Yet, if you feel a stock broker is evading his responsibilities, then it is a failure to comply with the rules of Securities and Exchange Board of India (SEBI). It has clear guidelines for stock brokers to run and close their business.
Ignoring your request would be a case of fraud. You can approach the SEBI or a court and file a lawsuit for breach of contract. There are several provisions in the law which shall provide you the required solution for your problem. In most cases SEBI deals with the broker and helps out the investors. To know more about the available legal options visit financial portals like Value Broking.