Actually it's not good to "end" any fast with the liver flush. Common sense dictates that you don't wanna dump a buncha oil and use a dehydrating chemical like the e salts in a system that has been at rest for 10 days.
The ideal course of action is to break the fast a prescibed and gradually start adding some oils/fats to your diet to get bile production going. When you are back to regular bowel movements that's the ideal time to do the Liver flush after any fast.
In these public forums you have no idea who's coming up with what and what they might actually know so it's no surprise that you might have read someone come up with the idea of doing a LF in the middle of fasting which to me just on common sense alone is a bad idea. This is not the first time and it won't be the last that people have talked about doing a LF in the middle of fasting on this forum.
Lots of folks out there with mess'o titles and theories so it's up to each individual to educate themselves and use their intuition and "common sense" to sus out through their experiences and the shared experience of others through forums like this what is best and what "makes sense"