I don't think this question has a straight answer, the answer depends on the person, the moment and what happened. Sometimes mistakes are made due to immaturity, some come from anger, some come from not knowing better until it's late.
Second chance can actually feel like a risk. Imagine giving someone that stole a company's money a second chance. It may look like putting the company's financial assets into danger.
Still I think second chance is something people are automatically entitled to. It can be earned again with positive actions and not only words. Some people just say sorry and expect everything to go back to how it was. It's easy to say "I'm sorry" but changed behavior requires an effort. And sometimes even when someone is sorry it doesn't mean you should take them back. Forgiveness does not resort to reconnection.
I also believe that people changes. I have seen it happen. They learn from their mistakes, rebuild trust and becomes a better version of themselves. Real change shows up in character not just in words.
So do people deserve a second chance? It depends on who did it, what he did and the situation that led to such action. If it was just a mere mistake then maybe second chance could be given.
The real answer isn't YES or No. Maybe it's this:
Some people deserve a second chance but not every situation deserves access to you again. And sometimes even when someone changes, It doesn't mean they have to stay in your life. So maybe the question isn't whether people deserve deserve a second chance , it's whether you feel safe enough both emotionally and mentally to offer it to them without loosing yourself again. Second chance should not be about them, it should be about you.