Provided the guarantee was properly executed (ie. signed and dated) then it will be binding upon you, your liability under it does not cease as a result of the landlord passing away I'm afraid.
They are highly unlikely to release you from it, particularly where the tenants have become in arrears with their rent because it gives them security in that they will be able to recover the arrears from you - this is purpose of the guarantee.
To seek to limit you liability I would engage with the landlord's son or agents and ask to be kept up to date with any continuing arrears. If the tenant falls in to two months rent arrears then the landlord could serve a s8 Housing Act notice giving the tenants two months to vacate. They would then be able to sue the tenants but they would only receive judegment on the rent up to the time at which the court decides they would have been able to re-let. This is better than them being concerned with the administration of the estate and letting the tenants rack up more arrears.
If however the guarantee only refers to the original tenancy and not any renewal or to liabilty during the course of the tenancy then it may not be enforceable against you. You have to check specifically the wording of the guarantee.
I would also suggest that you ask the landllord to contact the local authority to inform them that their housing benefit paid to them does not appear to be being used for rent.
Sorry it could not be better news.
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Edited by Thomas on 12/12/2010 at 1:31 PM EST