buying a flat, but tenant may not move

Rent Arrears

the vendor had an informal tenancy arrangement with a family friend to rent their flat.
They now want to sell the flat to us, but the "auntie" won't move as she now wants a council flat.

They tried evicting with S21, but this proved fruitless because there was no original AST (though obviously one could have been assumed, but then we're into legal wrangling)

The exchange of contract will push the auntie up the council's waiting list, as it will be clear that will is being made homeless.

The vendor has also agreed in a private arrangement to PAY the auntie to move out by completion date, and stay with her daughter.

You would THINK the auntie will move - but what if we exchange, but she doesn't move.

What do we do?
What compensation can we get?
Does it cost us anything in the end?
If the vendor cannot pay this cost, can it be deducted from the sale proceeds of the flat? (they will have already paid off the mortgage)

Obviously we've talked with our solicitor about this, but I'd like any more information or personal experience.

Many thanks,
Richard