Does it matter if the business has unpaid HST when I'm only buying the assets?

It matters, even though an asset purchase is generally designed to let you pick which liabilities you take on. In a properly structured asset deal, unpaid HST is a debt of the selling corporation, not something you agree to assume, and your purchase agreement should say so explicitly and require the seller to clear it (often out of the sale proceeds at closing, through your lawyer's direction to pay).

The practical risk isn't that you inherit the debt by contract — it's that an unresolved HST liability can complicate closing itself, since outstanding amounts owed to the Canada Revenue Agency can sit behind security registered against the seller's assets, or the CRA can pursue collection against the corporation after closing in ways that indirectly affect a business you're trying to keep running smoothly (disputes with suppliers, frozen accounts, reputational spillover if you're continuing under the same trade name).

Confirming the seller's HST filing and remittance status before closing, and structuring price and payout instructions so the debt is actually paid off at closing rather than left for the seller to "deal with later," is standard practice. A Treadstone business lawyer can build that into your closing mechanics.