suitable compensation or responsibility

She is the lone legal heir of her deceased husband, hence she only has full rights over the property after the demise of her husband.

She can refuse to vacate and she can also transfer this property to anyone of her choice either by a sale deed or a gift deed.

There is no compulsion on her to accept their offer.

Her husband's siblings do not have any rights over the property at least not during her lifetime

What is the basis / pretext for asking wife to vacate her flat i.e., why she may leave her property?

Facts posted are prima facie hypothetical. 

Sir

Thankyou very much for the prompt reply...

The flat is on the name of the bedridden person's husband and his mother. Since the mother expired 5 years back, won't the mother's share go automatically to her husband ie father in law of the bedridden person?

You are right that being one of the legal heirs, he shall be entitled to a share out of her share in the property.the legal heir  upon her intestate death.

Now upon his death his half share and his share out of his mother share shall devolve on his wife

The siblings of her husband cannot ask her to vacate or evict her forcibly.

She can give a complaint to police if she is forced to leave the house or she can file a suit for partition as well as injunction to restrain them from forcibly evicting till the disposal of the suit.