@Emily Powell , I am looking into this, too. I have heard that most landlords are insured through Texas Fair Plan (run by the State of Texas). They do not offer landlord liability insurance, so you'd have to purchase that separately, like @Waylon Themer said. Here is what I found online today:
From texasfairplan.org:
"As a market of last resort, coverage available through the FAIR Plan is not as comprehensive as coverage available through the voluntary market. The FAIR Plan does not compete with the private market and applicants must have two declinations from other insurers in order to obtain coverage with the FAIR Plan. Applicants are not eligible for coverage with the FAIR Plan if they have a current homeowners or other residential property policy, renewal offer, or a binding quote from an authorized insurance company.
Although the FAIR Plan is considered a market of last resort, applications submitted for coverage are subject to underwriting guidelines for characteristics of ownership, condition, occupancy, maintenance, and liability exposure. Properties owned/deeded in the name of a business (corporation, partnership, association, LLP, LLC, etc.) are not eligible for coverage with the FAIR Plan. Vacant/unoccupied properties are also not eligible for coverage with the FAIR Plan."
From a forum:
"As a homeowner there is really not anything to worry about they are a good company. As an agent they need to be turned down 2 times by other companies (as stated above). However, the commissions are very good for the agents so a lot of them want to cheat the system."
From same forum thread:
"We had them for our rental property in Houston since my normal agent (State Farm or Farmers, dont remember which) did not do rental properties.
A few years later the place burned down and TX Fair Plan paid the claim, + rental income loss."
I think it's possible that many insurers don't offer coverage for rental policies, so maybe the agent submits applications to those he knows will decline coverage then legally applies for coverage through Texas Fair Plan. If anyone here knows how that works, I'd be interested to understand more.
Another thing I read on the Texas Dept of Insurance website is that Fair Plan can't be used for vacant properties, so I don't know how that works when you are rehabbing the property.