Should I sign a short work authorization that does not spell out the price or repairs?

Ask what it authorizes before signing: emergency drying only, demolition, contents work or reconstruction. Get the scope, exclusions, price or pricing method, payment schedule and approval process for added work in writing. The contract should identify the contractor and estimated timing, with no blanks. Have unclear commitments explained and keep a complete copy. An insurer approving an estimate does not replace a clear contract between you and the contractor.