Make certain that you know the maximum amount your insurance policy will pay for the most severe incident.
When you pay your premium every month, put the same amount into a savings account that you never touch for any reason. When your account reaches the amount equal to the max payout for an incident, cancel your policy and keep chucking a few bucks into the account...BINGO your own insurance policy that will pay higher if needed, costs less than an insurance company, and if something DOES happen you won't get sued by an insurance company to recover their "losses" that you pay them for in the first place. If nothing ever happens, your kids have a nice inheritence.
This is someone who has no idea of what insurance is for. Yes get the liability. If you belong to IBM then is will cost you about US$120 per year with a US$2 million limit. As to the above rambling if you do need the insurance the company pays 100% of the loss and it will not, actually can not sue the insured for paying ouit for them.