It depends on the size of the company as to what needs to be documented to let someone go. SMBs can let people go much easier, and the smaller, the easier.

But what you cannot do in any circumstance is let people go "for any reason". There are laws against that at any size, and you are looking for a lawsuit if you give a reason.

It's best to just tell them their position has been eliminated due to restructuring (has to be provable if you're a big company), and give them no reason beyond that. If you don't give a reason, they have nothing to bring a lawsuit for.

In summary, reasons are not always required, but are always a liability.