The OC can still send monthly statements if they only contract the CA as an agent; in other words they do not sell the debt to the CA. As long as the OC still has ownership/possession of the account, they can send statements. Generally, if they are sending the account to a CA, then they have already closed the account, and would stop sending statements.
If the OC on a revolving account is adding interest and fees, they may have to send statements, under FCBA.