Yes, Claimable can notify you via email when a claim is closed or re-opened.

You can choose to be notified when the status changes either for all claims or only for claims assigned to you.

You will just need to ensure you have either the "Claim Status Changed (All Claims)" or the "Claim Status Changed (Assigned Claims)" notification turned on for your user account.

To do so, open the Notifications tab under Your Preferences and tick the box next to the correct notification option.