If they are hurt and don't want to remain friends and so walk away that's one thing. Because I think terming it as rejection is part of the problem. They aren't rejecting you as a person, they are saying that they don't want to date you. That can be for many reasons, both about you or about themselves. I spent a long time shut away from relationships because I knew I needed to get myself emotionally healthier and until I accomplished that, I couldn't be right for anybody. But not everybody who wanted to date me during that period understood that it was about me, not about them either as a person or as a potential partner.
But there is some number of people who won't be able to walk away. Some turn to hate (not the fault of the person who doesn't share their feelings) whether that's malicious rumor spreading or violence against either the target of their affections or other women like that guy who went crazy a few months ago in California who thought that women owed him sex.
Or as a friend of mine experienced, the guy who was told that she didn't share his feelings, just kept going. He would tell her that they belonged together, she would say no, we're just friends and she would get an email later saying that he had renewed hope that their relationship would last. It got to the point where he had to be banned from the gym as he wouldn't leave her alone and it was turning scary.
As with most things, you can't control the other person's response, only your own.