Who is liable for the deposit when property ownership changes?

For example, a tenant in a property puts down one month security deposit at the signing of the lease to landlord A. The property is sold to landlord B half-way through the tenants lease. Now the lease is up and I assume landlord B must honor the tenant's deposit refund as stated in the lease. At what point, if at all, do landlord A and B transfer of security deposit? Is this often overlooked? I can see this being an unforseen expense for landlord B if not properly addressed. Thanks, just curious!