If you reclass to 37F and don’t make the cut, do you go back to your old MOS or do you become an MP since you completed MP OSUT?

Usually you will be recycled and try to pass the class again. The Army want's you to pass.

If you reclass and don't pass your now MOSQ school you go back to your original MOS. If you don't have an MOS then you're not really a reclass. If you fail AIT and don't hold an MOS they can assign you a new one.

You go wherever they need bodies, good chance of the MP MOS, but it isn't locked in concrete- because they can even chapter you out.