The tenant once inducted as such will continue to remain as a tenant irrespective of anyone remaining there to take rent or not.
So there is nothing to worry .Since there is none who claims to be the legal heirs or assignor of the interest of the landlord your mother is under no legal obligation to tender rent to anyone though if she so wishes she can deposit rent in the rent control office.
However she can transfer her pagdi rights to anyone if any prospective buyers come forward with willingness to offer market price for the tenanted premises.