You may be able to keep her deposit--or at least such portion of it as is necessary to pay for the television. One of the purposes of the security deposit it to pay for the repair or replacement of the landlord's property, damaged or destroyed by a tenant. While the most common cause of such "damage" is physical damage, an appliance or other property of the landlord  is equally "destroyed" if the tenant takes it him/herself or unlawfully gives it to another, as it would have been had the tenant hit it with sledgehammer. Since you could apply the tenant's security deposit to a television she broke, you should be able to apply it to a television which she gave to someone else and cannot recover for  you.