It's difficult to imagine why they would do this, since it would remove all the cushion that 2+ week period would provide the company for getting projects closed and documented, and bringing new people on to take over the employee's projects. It turns an unfortunate situation into an immediate crisis.
I have seen (recently) a company say "please, we are begging you not to resign, would you like to take a sabbatical and we can talk about it when you're back?"