How to fix overlock plug?

Question

Electronics

Good afternoon, gentlemen of electronics. I would like some advice on what to do in this situation.
There is a sewing machine (overlock). It comes with a power cord (the pedal is also connected to it).
The problem itself is that the wire is constantly moving away (apparently due to the fact that it is oxidized, or burns out slowly) and does not allow it to work normally.
Here, in fact, is a photo of a mountain plug:

Also the socket into which it is inserted (the socket itself is attached to the overlock):

And finally, a couple of things that are still incomprehensible to me, but possibly useful for solving the problem:

• From the socket located on the overlock, despite the 3 visible "rods", only 2 wires go to the machine, from the outermost of these "rods"
  
• The pedal seems to regulate the speed of the torsion of the engine of the machine.
  

So, the task is to make sure that the wire does not leave and the machine works in normal mode.
Thank you.
----
The problem is solved, each of the commentators below was right in their own way.
The power cable and from the pedal have 2 veins (blue and brown).
I connected the blue ones and connected the brown ones to the overlock (brown from the power supply to the corresponding rod). Everything is working ;)

Answer 1

Cut and solder directly?

Answer 2

1. Most likely, there is a jumper between the 2 rods. They are interconnected.
2. Cut these connectors, solder the others. Whatever you choose, solder them.
3. If steps 1 and 2 are not clear, take a round needle file, clean the contacts from the inside and outside. Connect. Wrap the outside with duct tape so it doesn't fall out.