Something damaged while playing
The ball hits the window, a stone scratches the paint, a phone is dropped.
Your child is not liable — and you as parents only if you breached your duty of supervision. Where there is no liability, no ordinary liability policy pays. The injured party is left with nothing.
It depends on the individual case: your child is liable only if it had the insight to recognise the wrong. In a dispute a court decides — and until then it is open who pays.
Your child is fully liable. As long as it is unmarried and in education, your family liability policy usually covers it.