All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The tenant is entrusted with the leased property, but he does not guarantee what is damaged in it unless it is the result of his abuse or negligence.
Al-Shirbeeni said in Mughni Al-Muhtaaj: “The confirmed opinion is that the tenant is entrusted for whatever is leased, be it an animal, clothes, or else, throughout the period of rent; so he does not guarantee whatever is damaged from them unless he is negligent.”
Therefore, if the furniture was damaged due to the usual use (normal wear and tear) without any abuse or negligence, then there is no guarantee on you, and you are not Islamically required to pay anything to the landlord.
However, if the damage was due to any abusive usage or negligence, then you have to pay for the loss of furniture, and this should be estimated by the experts in the field.
This amount should be paid from your husband's inheritance before it is divided. However, if he did not leave any inheritance, or the inheritance is not sufficient to compensate for that, then you are not obliged to pay the compensation. Nonetheless, if you want to acquit your husband from any sin, as a way of donation from you, then you may pay to the owner of the apartment the value of what is damaged according to reasonable limits.
Allah knows best.