Unfortunately, no one can predict how or why a tenant will end their lease. In the unfortunate event that your property is occupied by a tenant that passes away, there are a few things that you should do to protect yourself and your property. 

1. Change the locks and secure the property. 
2. Let no one in the property without appropriate legal backing of their right to be in the property and to what authority they have to deal with what has been left in the property. 
3. Verify if there is power to the property to avoid potential problems with the refrigerator. 
4. Notify any next of kin you know or can find. This should preferably be done in writing. Let them know that the property has been secured and no access will be permitted without the appropriate legal authority to grant access. You can include any information as to the balance of any amounts owed and the term of the lease as the estate could be held liable for such. 
5. Depending on the response you get and how long it may take to resolve- consult with your attorney. You may need or want to take steps to have all the items boxed up or moved to a storage unit to await the outcome of any court, legal, probate, or estate settlement action. The expense of your attorney call could be added on to what the estate would owe for such expenses.

When in doubt, contact your attorney prior to letting anyone enter or remove any items from the property.