If someone injures themselves and sues, they will be suing the LLC and not you personally.

If someone dies, injured or permanently disabled in the illegal unit who pays for the defense and the liability claim?

In some areas if someone is encroaching on you, and someone gets injured on the encroachment, you can be sued too.This might be something to ask your attorney about in your area, and to clarify with your insurance company if they want a survey copy.Good Luck!

With the above being said, I am not an Oregon lawyer, but I did look up the Oregon Work Comp statute and the exact information you give, if the unlicensed handyman was injured at the home, he would have a great case to the work comp board and petition that he was your subject worker and thus is deserving of work comp benefits. 

If you want coverage for any of the following; Fair Housing, Wrongful eviction, Discrimination, Injured workers, Rented vehicles, etc., you would need to purchase additional policies

For instance, if a partner let's his kid drive his car and the kid gets into an accident and seriously injures someone, both partners can be sued.

They have asked us if we have any type of insurance that would cover any incident if my wife and I or any cleaner or handyman that we hire were to be injured on the property.   

I truly enjoy being a member of the Linville Central Rescue Squad mountain rescue team and helping people lost or injured out in the wilderness.

Glad no one was injured or worse.

And also avoid liability if someone gets injured on my property, so considering an LLC.