Car crashed into fence and damaged it

Hi All

Can anyone offer some help/advice, someone crashed into my relatives house they weren’t in and came home to find fence panels and concrete post all smashed up, the person responsible came to their house and said will pay but it has been nearly 3 weeks and haven’t heard again from them. There is no CCTV but neighbours witnessed it. They’re now saying to contact their insurance company and make a claim. Will insurance company pay? Any advice will be much appreciated, thanks in adv