GENERALLY, in the USA:
Let's say you crash your drone into your neighbor Peter's window and the drone goes through the window (free fall because the battery died). The window is broken and the drone is broken. Not only that, the drone hits Peter in the arm and he is bleeding a lot and has to go to the Emergency Room. What happens now?
1. PETER: He is really pissed.
2. LIABILITY: Your homeowners/renters policy includes a $100,000 personal liability protection (you can increase this amount to $300,000 for about $25/year in premium). This will protect you from liabilities resulting from damages that you cause with your drone. So your policy will pay to replace the window as well as pay for Peter's medical bills, up to your policy limit.
3. DRONE: If you have the standard homeowners policy, you get no coverage for your drone. You just need to buy a new drone. If you want coverage for your drone for things like this, you will need a Scheduled Property Endorsement (almost every policy has this option) or to get a separate Personal Articles Policy (like the one from State Farm or many other companies). Homeowners policy provides coverage for only specific perils whereas the Scheduled Endorsement or the PAP provides coverage from ALL perils unless specifically excluded.
Qualification: I was a full time insurance agent for 3 years and a part time financial advisor focusing on insurance for 3 years. I've seen hundreds of claims denied because people thought they were covered by something that they were not, including dozens of times when the agent told the insured that they would be covered. ALWAYS GET THINGS IN WRITING!