The following is an oversimplification, but should give you a basic idea.Some people (with large accounts) do own and operate de-comm'd military jets.
The radios, radars, and other functions must be brought up to your specific countries regulatory agencies requirements.
To overstate the obivious, the jet cannot have operational weapons systems. I have heard in some cases they may be allowed simulator equiptment, but again heresay.
To fly solo, you must have the proper certification. Which in the case of a jet, a standard single or multi-engine certificate will not suffice.
Whereas an organization such as FlyMiG would have different arrangements.
Foxhound: Good Luck.