Have the agent put their 'demands in writing' .. because they are wrong.
1) The bank owes you the security deposit.
"Assure tenants that the new owner is responsible for returning any security deposit: The
owner or agent should affirmatively tell tenants that the new owner is responsible for returning
any security deposit that the tenant paid when the property is vacated. The owner may not
refuse to return a security deposit just because it never obtained the money from the prior
owner. The owner or agent should not deceive or confuse tenants into believing that they must
pursue the former owner to get their security deposit rather than requesting the security from
the new owner. If a tenant is planning to move, then it is the tenantâ€™s obligation to provide a
forwarding address to send the security deposit to them after the move. However, owners or
agents should remind tenants to provide such a written forwarding address."
2) Cash For Keys:
"The entity that owns the property at the time a tenant moves out (usually the bank after a foreclosure) is liable for the return of the security deposit to the tenant, even if the security deposit that had been paid to a previous owner was never transferred to the new owner. It is untrue, and therefore may be an unfair trade practice, for an owner or estate agent to tell the tenant that the tenant must reclaim the security deposit from the former landlord. The Security Deposit Act also contains a number of provisions that, among other things, specify when a security deposit must be returned, the amount of interest to be paid on security deposits, the requirements for escrow of a security deposit, and what penalties exist for violating the Act."
"The Connecticut Cash for Keys Law (Conn. Gen. Stat. Â§47a-20f, as amended by Section 3 of Public Act 10-181) requires that if money will be offered to tenants to persuade them to move following a foreclosure, the payment may be double the total of the security deposit and unpaid interest, or two monthsâ€™ rent, or $2,000 â€“ whichever is greater."
3) If you have documentation that states you had purchased the appliances and would take them with you .. then stick to that claim. Your lease is valid for the duration.
4) I would get the name of the Asset Manager that the Agent is working for and tell them what is going on. If it was me I would refrain from dealing with the agent as they are not trustworthy.