I have a 4 unit building that is older but roof, electric and plumbing/piping have all been updated in the last ten years.

I may have had some minimal damage from roof leak, broken pipe etc, but not a single claim.

Say, you put $10,000 on a $50,000 house in the Midwest and you learn that you need a new roof and furnace and that the tenant has stolen all of the copper piping before vacating the property in the middle of night. 

My understanding is that hte umbrella policy is supposed to kick in after the underlying policy is exhausted. 

If you rent them out be prepared to handle freezing cold weather and frozen pipes, a big problem with them.

The inspection report of the main sewer line reads: "Pipe appeared to be operating effectively and there were no immediate emergencies identified.

Plumbers came out and found sewer pipes were clogged with tree roots.

Could you sell it for more if you advertised it as having new pipes?

So I would suggest that when tracking anyone's posts and wondering if what they say will hold water any better than a rusting pipe, you consider the following statement.

You may need to get a Vacant Dwelling policy to provide the needed coverage (vandalism, pipe bursting, etc.).