You don't need to go replacing the entire thing. You can get an underground wire locator and find breaks easily, then fix them with adding a bit of wire on a watertight connector.
Link to what you'll need:
https://www.amazon.com/gp/product/B01GDZLZOU/ref=ppx\_yo\_dt\_b\_search\_asin\_image?ie=UTF8&psc=1
https://www.amazon.com/gp/product/B07F9KH8PT/ref=ppx\_yo\_dt\_b\_search\_asin\_title?ie=UTF8&psc=1
This isn't going to do what you want.
This one might: https://smile.amazon.com/F02-Underground-Locator-Tracker-Earphone/dp/B01GDZLZOU/ref=sr_1_3?crid=1XY7WCUGMLEOP
I have that one, and I have something like what you asked about. The circuit tracers aren't designed to tell you where a break is, only where the wire you are looking for is. While it will sort of tell you where the break is, the accuracy is going to be lousy. The one I suggest is designed to do exactly what you want: find a break in a wire. It will get you within a couple inches of the break. But it's designed to be used with a real earth ground, and I'm not sure it will work with the ground in the same cable. You may have to use another wire a few feet away from the floor cord but following the same path as a pseudo earth ground. It's returnable if it doesn't work for you. I use it for the purpose it's designed for (find a break in an invisble dog fence wire) and it works really well for that purpose.
Now, a real TDM will tell you where the break is, in meters, from the end: https://smile.amazon.com/Triplett-TDR100-Length-Tester-Reflectometer/dp/B08BTKW2B1/ref=sr_1_12_sspa?crid=38T0P3DQ0QEG&keywords=time+domain+reflectometer&qid=1636592111&sprefix=time+domain+r%2Caps%2C176&sr=8-12-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExS0NNVVRQT1dVOTFRJmVuY3J5cHRlZElkPUEwMjYxMzUwWldNM0xCUjc3MThYJmVuY3J5cHRlZEFkSWQ9QTA2MDM2MDcxWjJZTUU3NUJJMVRSJndpZGdldE5hbWU9c3BfbXRmJmFjdGlvbj1jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ==
That will work for sure.
I have this cable locator: https://www.amazon.com/F02-Underground-Locator-Tracker-Earphone/dp/B01GDZLZOU
It didn't work for me with red and black both connected to the loop. It just made a solid tone over the whole loop as if nothing was wrong.
In order to work, I had to connect the red clip to the end of the loop that I took out of the red terminal on the base. The black clip had to be connected to a long screwdriver I stuck into the ground near the base.