Can I require the seller to settle certain debts before agreeing to a share purchase?

Yes, and this is a common and sensible closing condition in a share purchase, precisely because buying the shares means buying the corporation with all of its existing debts attached. Making payoff of specific debts — a shareholder loan, an old supplier balance, a line of credit you don't want to inherit — a condition of closing is a standard way to make sure you're not taking on obligations you didn't price into the deal.

The practical mechanics matter here. It's not enough for the seller to say a debt is paid; you typically want written payoff confirmation or a discharge from the specific creditor, particularly where a lender or supplier holds registered security against the corporation's assets. An alternative to requiring payoff before closing is holding back part of the purchase price at closing specifically to pay a debt directly, rather than trusting the seller to do it afterward.

Because the corporation remains liable for anything not actually settled, regardless of what the purchase agreement assumes, it's worth having a business lawyer build specific payoff and discharge requirements into your closing conditions rather than relying on the seller's general assurances.