No, I'm sorry, they can't get a refund. Let me explain why.
Insurance companies work like big pots. People pay premiums into the pot. Then, those people who file claims collect from the pot. Insurance companies are just middlemen, collecting money in the form of premiums and using that money to pay out claims.
You said your parents never made a claim on their home insurance. Then they are among the lucky ones. The premiums they paid were redistributed to the family whose house burned down and collected $600,000. Or to another family whose house was severely damaged by a tornado and received $350,000. Or to the family whose house was burglarized and vandalized and got $175,000.
Although your parents did not collect on a claim, insurance gave them the peace of mind of knowing that if something had happened to their property, the insurance company would have dipped into the pot and made them a payment using the premiums of others.
In such situations, you could ask your new agent to intercede for you. He or she can have you sign a cancellation request, attach proof of your new coverage retroactive date and send both directly to your old insurance company, bypassing the old agent.
I'm concerned about your parents now going without home insurance. I hope that they can soon find some assistance in the community to help them solve that problem.
All the best.