Who's responsible if the security deposit with the landlord hasn't been transferred by closing?

This should be addressed directly in the lease assignment agreement or the purchase agreement itself — either the existing security deposit held by the landlord is formally assigned to the buyer, usually with a matching credit to the seller reflected in the statement of adjustments, or the deposit is refunded to the seller separately while the buyer posts a fresh deposit of its own with the landlord.

If it isn't addressed and closing happens anyway, the seller technically remains the party entitled to that deposit from the landlord's perspective, which can leave the buyer needing to sort out reimbursement directly with the seller, or negotiate a new deposit arrangement with the landlord after the fact — both less clean than resolving it before closing. This is exactly the kind of detail that should be confirmed with the landlord and built into the lease assignment paperwork ahead of time, since it's a straightforward gap to close beforehand and a genuinely awkward one to unwind once the deal has already completed.