Can a secured lender's security interest survive if the borrower corporation is sold?

Generally, yes. If the corporation itself is sold through a share sale, the corporation's own legal identity doesn't change — the shares change hands, but the corporation remains the same debtor, and any properly perfected security interest against its assets continues exactly as before, unaffected by who now owns the shares.

If instead specific assets of the corporation are sold rather than the corporation itself, a properly perfected security interest can generally still follow the collateral into the buyer's hands, unless it's been properly discharged beforehand or the buyer qualifies for a specific protection, such as buying in the ordinary course of the seller's business in circumstances the PPSA recognizes as giving the buyer clear title. This is exactly why anyone buying a business's assets, or shares in a corporation known to have existing secured debt, should search the PPSA registry before closing — a security interest that isn't dealt with as part of the transaction doesn't simply disappear because ownership changed hands. Getting a payout statement and discharge from existing secured creditors as part of closing is standard practice for exactly this reason.