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As Contracts have been exchanged, both parties are legally bound to complete. Therefore if the Seller were to die before completion, his Personal Representatives/Executors of his Will are still under a duty to complete.
As I think you are aware, there would, however, be a delay in your Mother-in-law's receiving the necessary paperwork to register your Mother-in-law as the new owner at the Land Registry, as the Land Registry Transfer will need to be signed by the Personal Representatives and they will also need to obtain Probate, a copy of which will be required by the Land Registry.
In practice, what normally happens, to enable a Buyer to move in on the completion day, is that your Mother-in-law's Solicitor will request an Undertaking from the Seller's Solicitors that in return for him sending the Purchase monies, he will hold the monies to his order, pending receipt of the Probate and Transfer signed by the Personal Representatives.
I hope this assists you and sets out the legal position. Let's hope the above never needs to happen.