Do insurance companies drop/cancel your policy if youhave a lawsuit(premise liability) or demand letter and you havent report it to them? What are some reasons of why a insurance will drop you? Im talking about Home Insurance.

As a small business, I’m finally getting around to looking at business insurance. God forbid I should get sued, but that would be the only reason I would get insurance at this point.
If I get sued (assuming I did nothing wrong that would terminate coverage), what are my responsibilities with regard to paying legal fees? What role will the insurance company play or what control will they have in the litigation process?