Is the salary a person receives permissible or impermissible, given that he does not perform actual work at the institution where he is registered, and is he, or the owner of the institution, sinful because of this, or is there no objection to this action?

It is understood from the question that the owner of the institution intends to create a fictitious employment contract without actual work, in order to collect a state salary. This is forbidden falsification and deception, due to the Prophet's (peace be upon him) saying: "Whoever deceives us is not of us." It is impermissible to do so because it violates the conditions for entitlement to a state salary, which are a genuine contract and actual work. The Prophet (peace be upon him) said: "Indeed, there are men who delve into the wealth of Allah without right, and for them is the Fire on the Day of Resurrection."