As for my knowledge, all the candidates will be routed only through the recruitment agency. The agency will make follow up with the client and they will also be in touch with the candidates until they are on boarded.
All the communications will be shared with the agency regarding the candidates status.
But make sure to have proper agreement or PO or Work order stating all the terms on which the recruitment is done.
From India, Mettupalayam
In my experience, the Agency must be paid if the person is hired by the company within a certain period of time. The Agency would have recourse to legal action if the company has tried to cheat them by not paying the agreed fee.
From Australia, Melbourne