If your mother held stock in her name, over the past several years the company may have been sending her dividend checks or proxy materieals. The these items or any correspondence sent were returned to the company the company would then escheat any monies and or securities to the state in which you mother lived.
If she had stock with a brokerage firm, and any checks or certificates were returned for failure to be able to be delivered to her, these items (checks and certificates) would be escheated to the state in which she lived.
You should start with the state in which she lived and see if there is any "Unclaimed property" in the name of your moter. If so, the agency will help you filing the required paper work to claim the property
If you were to call the company, all request in for information must be in writing and you must provide proof of your relatioship to your mother along with a certfiied copy of the death certificate and a court provided "short certificate' Very seldom will any company provide that much information based soley on a phone call.
If you know the company she had stock in, then you can contact the company's investor relations office. They have records of all stockholders. If you don't even know what stocks she held, you are out of luck unless you can track down who her stockbroker was. There would have to be statements in her papers. If there are no statements and no certificates, chances are there is no stock.
You go thru her paperwork & find her broker. There is no stock database that you can search. Or you wait for mail, and/or e-mail from them.