Outstaffing (or agency work) is the registration of employees in the staff of another organization. People actually work in the same company, but according to the documents they have a different employer (outstaffing company).
The outstaffing company performs all the functions of an employer: pays wages, pays taxes, maintains personnel records, interacts with government agencies, and so on. But she herself does not conduct any activity, but only “rents out” employees to other firms. Most often, outstaffing employs laborers, labor migrants, and service workers. for example: https://peiko.space/service/it-outstaffing-company
Do not confuse outstaffing and outsourcing. The second is the transfer of some functions or business processes and tasks to a third-party contractor (for example, outsourcing of IT or accounting). With outstaffing, all functions remain within the company, but employees are formally removed from the staff.
The main risk for an employer is to run into an illegal outstaffing company. In this case, all sanctions for illegal workers, non-payment of taxes and violation of migration laws will fall on him.