So as a means of creating a safety net, I am considering the idea of owning a property and renting out.

I just purchased a home last month and got an owner title policy.

Are these in a commercial policy were you can only pick ACV or RC?

If you do not have a lot of real estate experience (pricing, advertising, purchase agreements, title policies etc) then I would advise hiring a real estate agent as they will work to protect your most valuable asset.

Our new policy is to charge a commitment fee to this type of borrower if they return in the future.

If there is going to be a wraparound (or Subject to) mortgage make sure you buy a title policy through a Trust friendly (build rapport for future reference and deals) title company as to satisfy The Seven-Day Notice Requirement: Sec. 5.016(c): "where the purchaser obtains a title insurance policy insuring the transfer of title to the real property" Even then, you are still closing a deal without protection of your assets.

I am thinking about an agreement that the renter/lessor agrees to accept responsibility for the safety of themselves, family, guest, and anyone else that they cause to be on the property.

You can enforce a clause, if present, in the LC that the Vendee obtain and hold proper insurance but you would still want a policy of your own.  

Not that I depend on this, but it's another nice safety net -- but insurance on the house/my stuff is my main safeguard.I let complete strangers who I thoroughly check.

The Staging company stated that they also have insurance, but he said it would affect their policy and put them in a high risk policy so he would rather get paid in cash.