The person will not press charges for check fraud, can there be a case?

Yes; whether the case proceeds is often up to the prosecuting authority and not the alleged victim. However, the prosecuting authority, whether it's the Department of Justice or a local city attorney, will certainly get input from the victim regarding whether they wish to proceed. If someone suspects they may be charged with a criminal offense, I'd recommend they retain a lawyer because what they say can and will be used against them if there is an ongoing investigation. Be especially wary of any potential interviews by police officers or agents.

Prosecuting a crime that involves a victim requires a victim. Without a victim who will testify the prosecutor will have to drop the charges. When the prosecution does not have a strong case the defense attorney may hold a preliminary examination. If the prosecution cannot meet their burden of proof at the hearing the case will be dismissed. Speak with an attorney before speaking to police.

Theoretically there could be but unlikely. The government brings all criminal charges but they would need the person's cooperation.

Yes. It is not up to the person to press or drop charges. This crime will be prosecuted by the State or Federal government, not the person. Also, anytime the FBI wants to speak to you, it is VERY SERIOUS!! You should obtain a very good criminal defense lawyer immediately. The consequences for a federal conviction of this type will haunt you for the rest of your life.

The can be a case if the bank is going forward or if the prosecutor is forcing the case to go forward. Your prospects improve where there is no witness to testify that they received a check from you.

Individuals do not press criminal charges. Under Michgian law it is the prosecuting attorney who decides if criminal charges are brought. In the Federal system, the matter is brought before a grand jury who decides if there is an indictment. In either case, there can be criminal charges even if the individual victim does not want anything done.

The victim/complainant of a crime does not get to control whether or not charges go forward, that is up to the prosecuting official, for State cases, the county prosecutor's office, for Federal cases, the US Attorney's Office. Simply because the victim/complainant of the check fraud does not want prosecution does not mean that their won't be a prosecution. Often, the victim/complaint can help persuade the prosecuting official not to press charges, and they can make a prosecution difficult if they don't cooperate, but they can't prevent one. The FBI does not get involved with any matters that are minor in nature. If you have been contacted by the FBI, you should talk to an attorney immediately.