That's what background investigations are for.
Facebook is far too public to be effective as a secret second life for employees of the prison system who dream secretly of living the thug life and have Facebook friend lists to prove it.
Facebook, Time points out, is not a private place. Facebook does more to exploit and invade the individual privacy of its members than the MDOC could figure out how to manage in a lifetime.
That does not mean the MDOC or any other employer has the right do demand access to your Facebook pages any more than they have the right to send an investigator to tag along while you hang out with the family, go out with friends or have a nice long shower to wash the slime of your bosses' disrespect from your skin at the end of the day.
List of employer privileges is long, but stops at the factory door
There are plenty of perfectly legitimate demands an employer can make in the workplace that are inappropriate, illegal or ridiculous in any other situation: forced overtime, bans or limits on personal email, text or phone calls, limits on break time or sick days, dress codes, scripts that customer-service or help-desk staffers have to follow word for word.
None apply when the employee is off the clock, with the possible exception of bans on alcohol or drugs for pilots, truck drivers and others who would become public hazards if they were to come to work still suffering residual effects of their time off.
None of an employer's privileges include the right to follow employees home and eavesdrop on their family or social life.
Measuring public outrage over erosion of privacy and individual rights by big corporations
It is now possible to measure the use of public ridicule to modify or cancel efforts to curtail the basic rights of individuals and put them at the mercy of corporations or authorities that will abuse those rights for profit, to improve their own operations or just for the hell of it.
Public ridicule applied in the interest of quashing corporate totalitarian tendencies can be measured in units known as the SOPA Sweep -- named for the Stop Online Piracy Act sponsored by Lamar Smith, a corporate-profit-worshipping Texas Republican who believes consumers should be punished for not complying with specious corporate claims and demands that have no force in law.