It is very unlikely that BSNL will be shut down. It may be sold to a private player but there is no way it is going to be shut down.
It is just too big and too relevant to be closed down.
HMT had become irrelevant in the recent years and hence is being closed down.
Who will pay/subsidize for all the free mobiles , landlines , broadband which the bureaucracy and ministers uses ?
So never ever a telecom company owned by government will close . Government only sells a PSU if its relevance in present day scenario finishes .
Don't worry Gov can take such drastic steps in India, because it's India. Closing all these biggies will cause enormous job losses=enormous vote losses=not going to happen. Sleep tight.