Yeah +1 on the monster comment. We need a dose of reality like that, even though you all know I like to dream sometimes.
You know those taban pics could also be the result of lens tricks and people making different expressions with their eyes. So proceed with caution is the right attitude.
My sister had a slight problem with her eyes, basically they wouldn't close properly when she was sleeping leading to dry eyes. She also had a slight "negative or neutral canthal tilt", I use the quotes because doctors don't actually use that term.
Anyway, I talked with the surgeon together with her, what he said, basically, was that there isn't one single procedure to fix that, it depends on a few anatomical details, most importantly is your under eye support. That can be measured by the orbital vector.
In her case it was positive, her eyes problems were entirely due to the soft tissue in the canthus, he fixed it, 2 years ago, with a canthoplasty, results have been stable. Her problem, according to him, was a low insertion of the tendon into the bone leading to lax skin, he cut it and re-attached at a higher position. She was also showing signs of premature ectropion.
That's something common in older people, she was 20, although it wasn't still considered ectropion and it was smaller than in the pic as that would demand a different surgery.
It was really interesting, he pushed my eyelid down and when he let it go it would go right back up, while when he did the same to my sister it would take maybe a second for it to go back up.
A full canthoplasty like she did is a bigger surgery than a canthopexy, I don't know the details about canthopexies but you don't cut the tendon. It's still not a terrible surgery, nothing close to jaw surgery, she was back at home the same day, had ecchymosis for around a week and now she has a very small incision line on the outer corners of the eye, she covers it up with makeup but it's barely visible because it follows the natural folds of the skin.
Now, when your orbital vector is negative it gets more complicated. You need to see why it's negative. Is it due to a lack of bone support, a lack of soft tissue support or is it because of eyes that are too big to the eye socket?
Some doctors will just put an implant, as shown in the pic, but my doctor said he tries to address each case separately. Implants, orbital decompression, fat grafting or (IIRC, I could be wrong) cartilage grafting. Followed by the canthoplasty.
I will not be posting her pics and we're from Brazil, if somebody really wants to come her we can talk in PMs but I will not publish the surgeon name in public.
On the other hand, if you want pictures member Picollo30 had a canthoplasty with similar results in Portugal. Check out his thread about jaw surgery, he told me he also had a canthoplasty sometime in the past and it fixed his much greater negative canthal tilt.
My main point is that, at least in some cases, it can be done although some doctors on realself don't make it that clear, some relevant entries:
https://www.realself.com/question/turkey-tr-rid-negative-canthal-tilthttps://www.realself.com/question/portugal-lateral-canthopexy-correct-anti-mongoloid-downward-slant-lateral# 
