Can a seller be sued personally, or only the company that sold the business?

This depends heavily on the deal's structure and who actually signed as "Seller" in the purchase agreement. In a share sale, the individual shareholder or shareholders are typically the contracting party under the Share Purchase Agreement and are personally bound by its representations and indemnities — a buyer generally can sue that individual directly for a breach. In an asset sale, the contracting seller is usually the corporation that owned the business under the Asset Purchase Agreement, so claims are generally directed at that corporate entity rather than its individual owner personally.

An individual owner in an asset sale can still end up personally exposed where they gave a personal guarantee or a separate personal indemnity as part of the deal, or in the narrow circumstances where a court is willing to disregard the corporate structure entirely — something courts do only reluctantly and on specific evidence, not routinely. The starting point for answering this question is always the signature page and the defined "Seller" in your specific agreement, not a general assumption either way.