Can I be sued for rent after closing if the landlord never actually signed off on the assignment?

Yes, and this is one of the more serious risks of closing a sale without formal landlord sign-off. If the lease requires consent to assign and that consent was never actually obtained, the assignment to your buyer may not be effective against the landlord at all — meaning you can remain the landlord's tenant of record, fully liable for rent and other lease obligations, even though your buyer is the one operating from the space.

This can happen when a seller and buyer proceed on the assumption that verbal approval, or the landlord's apparent acceptance of rent from the buyer, is good enough. It usually isn't. Without a proper written consent (and often a formal assignment agreement), the landlord can treat you as still on the hook, and can potentially treat the unauthorized change of occupant as a lease default in its own right.

Never close a business sale involving leased premises without confirming, in writing, that the landlord has formally consented to the assignment. A Treadstone business lawyer can confirm the consent is properly documented before you let closing proceed.