Can a seller demand a share pledge as security instead of just a promissory note?

Yes. An unsecured promissory note leaves the seller as just another unsecured creditor if the buyer defaults, so it is common for sellers to negotiate additional security to back a vendor take-back, and a pledge of the shares purchased by the buyer, giving the seller the ability to reclaim or sell those shares if the note is not paid, is a recognized way to do this alongside or instead of a registered security interest against the business's assets.

Whether a seller can actually obtain this kind of security in a specific deal depends heavily on negotiating leverage and, importantly, on what any other lenders financing the buyer's purchase will permit given their own priority requirements — a bank providing senior financing may object to, or require subordination of, a seller's share pledge just as it might for other vendor take-back security. Buyers evaluating a demand for a share pledge should understand it as a real, negotiable security interest with practical consequences on default, not a routine formality, and should coordinate it with any other lenders involved in the deal.