property. Deeds are the legal documents that transfer title from one person to the other, and are recorded with the County Recorder. This is why you get "Title Insurance" - to insure your ownership and the right to use your property. This prevents other parties from laying claim to those rights. It's also why many lenders require title insurance, so they have proof no one besides the person to whom they are lending money has any claim of ownership to the property. Basically title can't be stolen, but it can be falsified with a forged deed. Having a $0 HELOC isn't going to protect you from forgery.
If you're worried about it, most title companies will do an O&E (owners & encumbrances) report for $50-$150. It's an uninsured report that shows who owns the property and what liens are showing. Or visit your County Recorder and ask if they'll so how to search the records on your property