As stated above, a policyholder can be negligent. For example, if a tree fell through the roof of a policyholder's house, according to their insurance policy, they are required to try and prevent further damage. Adding a tarp to a roof would prevent further damage until the insurance company could come and complete the claim process. If the policyholder decided not to try and prevent further damage to the roof, that could be considered negligence on the policyholder's part.
Another party besides the policyholder could also be negligent. An example of auto insurance negligence would be a driver following too close to the driver directly in front of them. We all know what this can lead to... the close following driver crashing into the person in the front. The driver that was following too close would be the negligent one since a reasonable person would not drive right on the bumper of the driver in front of them.
Insurance companies and agents can also be negligent. When purchasing a new policy an insurance agent is required to help the policyholder understand what they are purchasing, especially since the contract is written by the insurance company. If the insurance company or agent fails to disclose information about the policy, the company or agent could be negligent.

