I have to say in all my years of lending I have never seen a business purpose lc booked under a consumer purpose line.
Nor have I ever seen an lc that said if the bank deemed itself insecure the customer had to provide a demand note. For security, we took collateral. Some lcs contain language that converts the lc to a note upon a draw. Generally they will be issued under business lines of credit and blocked.
I've always documented a line and reserved a portion (or full amount) of the line to support the issuance of the letter of credit. If the line has a maturity date, the letter of credit must expire before or at maturity of the line. If the letter of credit contained an annual automatic renewal, the expiration of our cancellation option must be prior to maturity of the loan.
I’ve honestly never considered issuing a Letter of Credit backed by a HELOC. My gut instinct is to say no, and require a business line be opened up. I have nothing that says it can’t be done though.