Legally, yes, you can sell a house with an unsettled claim. If the claim could expose any buyer to any liability or lien, you'd have to disclose that fact (to avoid defrauding the buyer), and you should keep *all* records that may be relevant to the claim (even if that means keeping documents you'd otherwise dispose of); you should also disclose the pending sale to the insurer once you market the home so that if they need access to the home for any reason (e.g. any investigation not yet complete), they can do it while you are still the owner.