will they do investigation on your employment (call them )
Yes . . . While they may not call your RECENT employers, they will mail them a questionnaire to fill out. They may then contact them by phone to clarify the answers to any questions.
Just want to add to EdFarmerlll
If your company/corporate have an HR function to handle it, fill in the information that provided by HR to handle the employee record release. I made a mistake to put in my manager, and I had to have a minute to explain as manager got caught off guard. If you have no choice of HR function, then you might want to have a ‘talk’ with your manager what to expect and that you need him to complete and turn in if he receives one from OPM.
also will they see if a person was on unemployment
Yes, when you meet with a BI you will explain why you had x time of unemployment.