There are three statuses for offer
Disbled status - Offer is invisible and all the publishers links for disabled offer won't work. So the traffic stops immediately after setting this status.
After the click affiliate will get this message.
Paused status - Offer is invisible and all the publishers links for paused offer won't work. The traffic which has been sent before the offer is paused will be counted by Affise.
Active status means that offer is visible for everyone and works as usual.