Is anyone aware of a company like this that exists?
The problem:
You want to hire the best, and sometimes the best person is not willing or able to move to your country. International employment law is very complex.
You want to access hires who are not willing to work as independent contractors / freelancers, or you want to hire a long term member of staff and would prefer to hire someone who likes to work perm.
Solution:
This company has virtual offices all over the world, and will hire your perm staffer, or create a company for you to hire them through. They handle the legals, payroll, etc - like an agency, and always use your branding to communicate with the new hire, giving them a direct hire experience.
You advertise the role as a direct hire, so the existence of this company is largely transparent to the employee, and hopefully they are contracting with a local branded ltd that was set up for you.
Contracts between your company and the hiring company ensure that you are on the hook for any obligations the hiring company has to their employees.
Umbrella companies exist, and agencies exist. This is really just an umbrella with a bit of a branding twist and more mutual obligation.