|Been a while but I am pretty sure that you can configure your DHCP server to require that the IP change.
Basically the client computer asks for a new IP from the DHCP server and it is allowed to suggest a prior one. The DHCP server and accept that request or reject it and send back the one it wants.
So one can set up a rule in the DHCP server that forces a new IP based on other criteria.
That means nothing the client does, normally, would allow it to 'set' a static IP. Even if a user sets it up that way the DHCP would refuse.
At least at one time this was a common security constraint.