I don't think it's common either way. After a rejection, some people try to improve themselves, which is great. But after being rejected I doubt that most people would give the person who rejected them a second chance. When you reject someone, that's it. You shouldn't expect to have another shot in the future with the person you rejected.
Either way, I've seen both guys and girls improve after being rejected, and it is a very good thing. But they should stick to their pride and never forget who rejected them, not giving them any further chance.
Girls all the way... Girl not only try to loose weight, change their style up, change their hair color or whatever to try and get a specific guy that rejected them but they also go back and try to get guys they rejected themselves because they didn't know how they feel at the time and he's like fuck it and she's like I want him so bad now...
guys are taught to stand up... girls are often not.
Guys will commonly lower their standards a lot in order to get laid. As such there are very few cases of men rejecting women compared to the number of women that outright reject men. As such it is far more common for women to go back to men. That is until the men have careers are are stable, and the woman is either childless and desperate to start a family before it is too late, or the woman has several children to provide for and looking for a husband to help pay for everything.
I was recently contacted by a girl I knew in high school because her standards were so high, that she is digging through every guy that she rejected to find one to give her a chance now. I have never once had the urge to go back to a woman I rejected. There was always a good reason I rejected them and I stand by those reasons.