something along these lines

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Note added at 1 hr (2015-02-05 13:50:39 GMT)
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One company - the lessor - leases its employees to the leasing company - the lessee.

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Note added at 12 hrs (2015-02-06 01:02:29 GMT)
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"Leased employee" or "worker" means a person performing services for a lessee under an employee leasing arrangement.
"Lessee" or "client company" means an entity that obtains any of its work force from another entity through an employee leasing arrangement.
"Lessor" or "employee leasing company" means an entity that leases any of its workers to a lessee through an employee leasing arrangement.

http://www.ilga.gov/legislation/ilcs/ilcs3.asp?ActID=1259&Ch...
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Employee leasing company" or "lessor" means an entity that grants a written lease to a lessee pursuant to an employee leasing arrangement;

http://www.lrc.ky.gov/statutes/statute.aspx?id=32531