I had a skin tag on my neck for years, it was quite large.
On Friday I did the zip up on my jacket and felt a sharp pain – I must have caught it in the zip.
On Saturday, Sunday and yesterday (Monday) it was really sore to touch and was red and inflamed.
Today I woke up … and it was gone! No more pain, and it seems to have just fallen off in the night.
Will it re-grow, or not? Accidental skin-tag removal!

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It will most likely not grow back, depending on the things I list later in this answer.
I had a raised freckle on my face on my chin, and one day while I was trying to exfoliate my terribly dry and flaky skin, I accidentally scrubbed a little too hard and took the freckle right off. It hurt like the dickens, got red and inflamed, bled a little, and then closed up. There was no freckle for about a week or two, and then one day I noticed the spot was getting darker, and then BAM! My freckle was back just as it had been before.
On the flip side, my mom had a mole on her collarbone that she irritated, which then started weeping fluid for a day, got really dry for a couple days after that, and fell off a couple months ago and has yet to regrow. Her dermatologist says it never will grow back. I also had a skin colored mole in my armpit that had been there for at least 10 years. One day a few months ago, I was in the shower and as I was shaving I noticed it had turned from skin color to bright red. I assumed I had irritated it with my razor. The next day it hurt a bit and turned darker red. The following day it was purple, and the next day it was black. Finally after a couple days it just fell off and hasn’t grown back yet. Dermatologist says it probably won’t. Both this and my mom’s mole were moveable, meaning if we took a finger and pushed sideways on the mole it would be able to be pushed side to side, so it was fairly raised from our normal skin, whereas the freckle I have isn’t moveable and is very close to my skin.
(This is the list I was talking about at the top) It just depends on how much of the skin tag was actually attached to you under your skin. If it was raised high off your skin (like our moles) and was easily moved if you pushed it around with your finger, it probably will not grow back. If it was closer to your skin (like my freckle) and not easily moved around, then it may grow back.