If an employer asks an employee to move to a higher cost-of-living area then they're asking the employee to take on extra expense for the benefit of the employe

If an employer asks an employee to move to a higher cost-of-living area then they're asking the employee to take on extra expense for the benefit of the employer. It's only reasonable that the employer would offer some form of compensation if they want the employee to grant that request. If an remote-work employee wants to move to a lower cost-of-living area it should make no difference to the employer. They're still getting the same work as before, at the same cost. If the work output was worth that much before then it's still worth that much when performed from a different location. If an employee chooses to move to a more expensive location, on their own initiative, then that is more like the second scenario than the first, and there is no reason to expect the employer to offer higher compensation to offset the cost-of-living in the new location when there is no particular benefit to the company from the move. EDIT: fix typo