This is to protect your investment.

Demand, location, positive cash flow whether you are financing it or not, area growth, amenities, repairs, seller motivation, is it in a flood plane  economical pluses or minuses, property age, layout, historical issues, future projections, neighborhood issues, weather issues that are negative or positive, distance from an existing public protection, if provided, storage area, and property taxes. 

Do you think it should cost pennies for someone to give you millions of dollars of protection?

If source of income locally for you is a protected class you can not say that.

Part 1 of 5: What is a Deductible Buy-Down ProgramDeductible Buy-Down programs are insurance policies a business/real estate investor can implement in their protection plan to lower the amount of deductible they have to pay when there is a claim made.These are policies which are in addition to the normal coverage plan (property, liability, auto, umbrella, cyber, etc.)Part 2 of 5: How Buy-Down Programs WorkThey are one of many ways a person/business can implement alternative insurance protection.Buy-Downs are added to protection plans to lower out of pocket expenses for the insured at the time of loss (a claim)Example of how a Buy-Down program works:You have a commercial property portfolio.Its insurance policy has a deductible and a premium.

@Naveen Desai My hunch is no because all PPMs are written from the perspective of protecting the GP in the case the worst happens.

Or do I just need to make sure that the contract is worded properly and protects my interests?

The tenants are responsible for reporting issues to you so you have an opportunity to take care of the problem, improve their living situation, and protect your investment. 

Is an umbrella policy going to offer us adequate protection? 

The downside is you will need to live there, for a minimum of one year (to satisfy FHA Requirements); AND because you closed personally, you will not have Asset Protection, in the form of closing in the name of a LLC.