Bathroom Light Fixture with no stud or box
I found almost that exact same image behind a bathroom vanity light fixture that I took down to replace. Needless to say I was flabbergasted that such garbage workmanship would be hidden behind a fixture. 

You should look very closely at what is just behind the place where the romex cable is coming out one hole and reentering the wall cavity at the slot on the right. 

 

Mine looked exactly like that and there was a stud right behind that cable loop. 

I opened up a hole to the right of the stud for a suitable metal electrical box. I then drilled a hole through the center line of the stud from side to side and worked the wire through the hole. I then mounted the electrical box to the side of the stud and brought the electrical cable into the box and secured it with the box clamp at the rear of the box. Now it is properly wired but I had to work at finding the proper lighting fixture that would cover up the messy slot in the drywall. (I would have patched and painted it but decided to wait till I give this bathroom a facelift remodel in the near future.