Can an employer terminate an employee or ask him to resign as an apparent disciplinary action with a hidden intention to reinstate him by overturning their termination or resignation afterwards before the departure of the employee?
This sounds like they are trying to achieve a goal that will deceive somebody. It could be done to make them a new employee and qualify them for a benefit, or to eliminate their qualification for a benefit. They could be doing this to manipulate their employee count on a specific day. They could be doing this to claim they punished them, but then reinstate them after people stop looking.
All of these could result in real disciplinary action if it is discovered.
If you ask an employee to resign, any reasonable employee will just say “no”. If my company fired me, I can guarantee that I wouldn’t return for the same salary.
I once had an employee tell our whole team of about 20 people that our department would be closed. They made the mistake of waiting until the next morning to tell everyone that they had plenty of work in other departments. By that time I had already a verbal agreement for a new job.
Not a lawyer, and depends on jurisdiction, but I'm pretty sure this is one of those no taksies backsies things. When a job is terminated it's terminated - it's one party deciding to end the contract with the other. A "reinstatement" or reversal would entail a new job offer and would have to be agreed by both parties since slavery or indentured servitude is not a thing in most civilized countries.
Basic contract law in probably all civilized countries states that two parties can agree on anything that is not against the law.
So if the employee and employer want to agree on something, being it reinstatement or contract dissolution without notice period or free ice cream, they can do so.
Termination of a contract requires only one party's consent assuming all the constraints of the contract are followed (for example notice period).
So yes, in theory, if both parties agree they can do a lot of things. They can terminate employment and reinstate it daily. Even every minute if they can read, understand and sign the contract fast enough. There is no limit to what you can do if you cooperate.
But that does not really make a lot of sense, does it? You probably want to reach a specific goal. Whether that goal can be reached by your contract shenanigans? We don't know, because we don't know what it is.