Permanently and exclusively?
Happened to an agency I once worked at. We sent 6 people (4 were full time, 2 were contract) to a client to work on their project. After a year, none of the 6 people were still with the agency. The contractors were let go after the contract expiration, 3 of the 4 full timers took jobs with the client, and I left for another company.
Better off is software consultancy groups. They're more used to this set up.