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.  

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.

Liability: I firmly believe that every landlord should have an umbrella policy.

Than I found out it was an awful idea becauseviolated the mortgage (not a big idea now but gave mortgages a reason to come after you in a couple of years when rates were higher)no seperation- we self managed so we were unable to hide behind the llc, had we not been managing it, it would have been differentHard to get a Umbrella Policy- If it is under an llc you needed to have a cooperate policy much harder.Honestly we just have all of our houses under our personal name.

However, it is worth asking the question ahead of time to see what the bank's policy is. 

Foremost will allow you to add as many as you want to one policy, although I don't know of a major price break or discount that isn't simply just the multi-policy discount. 

Get a good insurance policy and forget all about the LLC hype that gurus teach because an LLC or trust will not protect you if someone sues you.Joe Gore

In general it is a very good policy.

It's just a policy I have for myself.

That was with Allstate, who also has my primary and auto policies.