Hi Liwen
Our mouth produces saliva all the time, and we unknowningly will swallow these saliva automatically. Drooling (dripping of the saliva out of the mouth) can be due to increased saliva production, or loss of control of the swallowing muscles.
Does your mom ONLY drool when she is watching television? And at other times she is fine? Perhaps she is watching a very engrossing TV drama and she forgotten to swallow the saliva, or perhaps the TV show features literally mouth watering dishes and that simulates her digestive system running. If she is not drooling when she is not watching television, I will not worry that much.
However, if she drools all the time, with or without watching TV, then there may be a problem with the muscles that control swallowing. It can be due to a stroke, or it can be a nerve infection.
Either way, it is still better to bring your mom to a family doctor for a detailed examination, and perhaps even some blood tests, to make sure it is not a stroke and she is not at further risk of one.
Regards