There is rarely full coverage during a local removal process, but many companies will cover for lost or damaged items due to negligence. However, it’s always essential that you read the Terms & conditions of the company to make sure you know what is covered and what’s not for the removal. If the initial coverage of the company isn’t enough for you, it’s possible to get insurance specifically for the removal process.  Pro-tip: take pictures of the most valuable and fragile items just before the move so you can have proof if something does get damaged or lost.