As you know, before you were first awarded a Section 8 voucher, a criminal background check was completed. If you decide to use the portability option, and your housing authority has determined that you are eligible to move, the new housing authority may complete a new criminal background check.
If you acquire a criminal record after you were awarded that first voucher, and the type of charge and/or conviction that shows up is unacceptable for the voucher program, the new housing authority may decide to reject your voucher and you would not be able to move.
You will get the chance to dispute the criminal record and to appeal the decision. However, you still might not be able to move.