Can a seller be forced to carve a piece of the company out before I buy the shares?

Not "forced" in a legal sense before any agreement exists, but it's entirely normal to make a pre-closing carve-out a condition of the deal itself. If you only want the corporation without a particular subsidiary, asset, or liability, you can negotiate the purchase agreement so that completing that carve-out — transferring the unwanted piece out of the target corporation — is a condition the seller must satisfy before you're obligated to close.

The nuance is that a carve-out isn't usually a same-day administrative step. Moving an asset or subsidiary out of a corporation can itself trigger tax consequences, require its own board or shareholder approvals, and need proper documentation, so it needs real lead time before closing, not a last-minute instruction. It's also worth confirming the carve-out is done cleanly enough that you're not later dealing with disputes about whether something was actually transferred out or just informally set aside.

If a carve-out is important to you, raise it early in negotiations rather than after a purchase agreement is largely settled, and have a business lawyer build it into the agreement as a defined, verifiable closing condition rather than a vague understanding.