Do leases terminate upon a tenant’s death?

Sorry to hear about your mother.

Unfortunately, a tenant's death does not terminate a lease.  Your mother's estate will be liable for the rent for the balance of the term of her lease or until the apartment is re-rented.  The landlord is required to mitigate (minimize) damages by making reasonable efforts to find another tenant.  The landlord has to mitigate (minimize) damages (the amount the landlord claims is owed). The landlord cannot allow the apartment to remain vacant for the balance of the term of your mother's lease without making reasonable efforts to find another tenant.  If the landlord does not make reasonable efforts to find another tenant, the landlord has failed to mitigate damages  and the landlord's damages will be reduced accordingly.

Reasonable efforts on the part of the landlord to find another tenant will be determined by what other landlords in the area are doing to attract tenants; for example, posting a sign on the property advertising the vacancy, advertising the rental in the newspaper, online, in a local rental guide, etc.  When the landlord re-rents the apartment, the obligation of your mother's estate to pay rent ends.  If the landlord charges the new tenant less rent than your mother was paying, your mother's estate may be liable for the difference in rent for the balance of the term of your mother's lease; however, the landlord has to have a valid reason for charging the new tenant less rent such as market conditions.  If the landlord does not have a valid reason for charging less rent to the new tenant, your mother's estate is not liable for the difference in rent for the balance of the term of her lease because the landlord has failed to mitigate damages and the landlord's damages will be reduced accordingly.