Now this is a very interesting question that I personally have experience with.
As I have a large cutting scar on my left eye, I can't open my left eye. The eye works, but I can't open the eyelid. I use a left forward stance, even though I am left handed. However, I don't do boxing. But it doesn't matter. The eyesight isn't that much different when 1 eye is closed. It just needs a bit more adjustment. If you look at the range of sight 1 eye has, you will notice that a big portion overlaps.
Now keep in mind, you don't have one eye at the back. You face your opponent, no matter which of your hands or legs is in front. Rather than adjusting your stance based on your own sight, adjust it based on your opponent's quirks.
For example, if your opponent is likely to use right hooks, and your left eye is bad or blind, you might benefit from changing your stance. But in a different way than you might expect. It's not as simple as changing which leg or hand is in front. When I fight, even though my left eye isn't able to see, I put my left leg in front as well as my left hand. This allows me to make up for the lack of eyesight by shortening the distance to the opponent's attack. This works especially well if the opponent is right handed. If my opponent is also left handed, I switch to something more orthodox. I do keep my left leg and left hand in front, but I angle myself differently. Instead of facing my opponent directly, I angle myself more towards their dominant hand. Yes, this creates a bit of a blind spot to my entire left. But this is where mind games come into play. Fighting isn't purely strength, technique and reflexes. It's also mind games.
They see a very easy to strike area for their right hand. But since their stance is right foot front and dominant hand back, they can't utilize it properly. In the time they use to decide whether to take the chance or not, I strike. Confuse your enemy with your stance. Don't change it to benefit yourself, but to disadvantage your opponent.