Does homeowners insurance cover renters belongings when their house was broken into and items were stolen?

If you are the owner of the house, and are renting to tenants (making you the landlord), then you only have insurance on the house (dwelling coverage - not homeowners coverage) and not the personal contents of the renters. In this case, no, your insurance will not cover their loss. It is the responsibility of the renters to purchase insurance coverage on their personal belongings.

If you are the renter (tenant), then you have to buy contents coverage on your personal belongings, such as furniture, clothing, etc. The landlord is not responsible for your belongings, whether the loss is from robbery, fire, etc.

In order to purchase homeowners insurance you have to own the home (but it can still be mortgaged) and you have to live in the home. Otherwise, you have to have a dwelling policy on the house if you want it insured, whether it's vacant or rented. If, however, there is still a mortgage on the house, the bank (or mortgage holder) will require you to have insurance on it.

If the house is paid for, then it is at your discretion whether to have it insured or not, for the value of the house. But if you rent it out, your state may require that you carry liability insurance on it.