Does Employee occupant need to sign lease?

[Henley H.]

We have  a company that would like to rent our property on behalf of an employee who will occupy it. The company representative will be financially responsible and the company name will be on the lease that is signed by the president of the company. 

Does the employee who'll be living at the property also need to sign the lease, or is it alright to just have the employee listed by name as a "tenant"?

The owner of the company has indicated he can't ask his employee to sign the lease, indicating financially responsibility, because he feels it would be unfair to the employee in the event the employee is fired or something...