Is renters insurance required if you do not pay rent?

The insurance company doesn't really care if you pay rent or not,they only care about what sort of policy coverage is on the property.

So the answer to the question is "it depends".

If you're not paying rent because you're living in your parents' basement, then there's a good likelihood that they have insurance that covers the contents as well as the dwelling itself. Check the policy to be sure, and also make sure that your property is not the sort that's typically excluded from coverage (for example, jewelry may not be covered under a standard policy).

If the property owner only has the dwelling itself insured (which may be the case if it's a property someone is letting you live in rent-free as opposed to them allowing you to live in their personal home), then your stuff is not covered; if it burns up, too bad for you, unless you have renters' insurance.