What happens if the business I'm buying is actually held in a family trust instead of direct shares?

If the corporation's shares are held by a family trust rather than by individuals directly, your actual seller is the trust, acting through its trustee or trustees, and the purchase agreement needs to be signed by whoever has the legal authority to sell the trust's property. Confirming that authority before you get too far into negotiations is essential, since a trustee generally can only act within the powers the trust document actually gives them.

The nuance is that a trust can have its own conditions attached to selling its assets — a requirement to get beneficiaries' consent, restrictions on what the proceeds can be used for, or provisions about how or when trust property can be sold at all. Skipping over this and treating the trustee as if they had the same free hand an individual owner would have can lead to a deal that isn't actually valid, or that a beneficiary later challenges.

Because reviewing a trust deed is a different exercise than reviewing a shareholder's personal authority to sell, it's worth having a business lawyer specifically confirm the trustee's power to sell, and whether any consents or conditions in the trust need to be satisfied, before you rely on their signature.