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In reply to the discussion: Massachusetts bill would require gun liability insurance [View all]slackmaster
(60,567 posts)...for an individual. Anyone who has any assets worth protecting should have personal or professional liability insurance. You never know when a banana peel you dropped accidentally can cause someone to slip and fall and be injured.
You can find a link to insurance specifically for that purpose on a site that I would prefer not to link to. But you can probably figure it out through Google.
BTW, my renter's insurance policy paid out for damage caused by a member of my household who wasn't related to me, but his name was on the lease. I'm not sure the concern raised in your subject line is necessarily valid. I believe a standard renter's policy covers liability for all members of the household.
If a renter has a person living in the home who isn't on the lease, that may be a point of contention with the landlord. Lease agreements are usually very specific about who lives there, and how long guests can stay without being reported to the landlord. Especially when the landlord is paying utility bills.