HELOC customer fears someone got her mail.
She is fearing identity theft. If this was a checking account we could close the account and open a new one.

Do we do the same with a loan? Does the entire loan need to be re-documented?

If access to the HELOC is thru the DDA Account you should just be able to get her a new DDA Account/Checks. The HELOC does not need to be redocumented. The HELOC just needs to be "pointed" to the new DDA.

Access to the HELOC is through checks drawn directly from the line of credit. No checking account is involved.

Since the loan number drives the transaction - change the loan number and order new checks (i.e. creating a new number and "moving" the loan over. The customer shouldn't have to sign new docs and the bank shouldn't have to carry the burden of producing new docs. Document the file of the history of what happened. The customer would feel much better.