Yes, they do. The at-will employment laws are not abridged by offering assistance to those who lost their job through no fault of their own.
The unemployment compensation is designed to give good workers assistance while they find another job. It is not meant to be welfare. That is why one of the requirements of the benefit is that you be actively seeking another job. It is also why the benefits are temporary, usually only 26 weeks.
And none of that does anything to change the relationship between employer and employee.