Sorry @Dede0 I wouldn't agree with this advice.
As has already been advised above. Just confirm to your guest that he needs to cancel his reservation. Tell him he can make a claim under extenuating circumstances with BNB for a refund, but that the sooner he does this, the sooner you might be able to relet the space.
Its only a click or two of a button for him, so if he can message you to say he isn't coming, then he can click on a button to tell BNB he isn't coming. They will then ask him for proof of his MIL's illness to consider the refund.
Good Karma for you in telling him this option is available. It's up to him to follow through with BNB if he wants to be considered for a refund.
He can of course also claim in his travel insurance.
Please don't offer him any refund of your own volition. Unscrupulous guests have been known to claim illness or death to get funds returned to them, when they cancel a booking.