Depends what you mean really. Are we talking about genuine repentance here? Are there certain things that even genuine repentance won't atone for?
Firstly- how can you be sure they're genuinely that sorry? That they've genuinely changed? If an action/crime is that heinous and they have in fact genuinely changed into a moral person- would they even be able to forgive themselves now? Could they even live with themselves?
I'm kind of suspicious whether all claims of repentance are that genuine. Especially when it comes to criminals serving time and making appeals. Of course they want to look like they're sorry and they've changed. They want early release! Not to say it's impossible of course but I think it's a difficult thing to judge- which is incredibly dangerous when it comes to psychopaths who are very good at mannipulating people and masking who they really are.
I guess it's largely up to the person that they inflicted the damage on to some degree. (If they're still alive.) Obviously- it depends on the misdemeanor. Say someone is unfaithful in their marriage though. If their partner forgives them and takes them back and seems happy (which I've witnessed,) who am I to judge them? It's like- they forgave them, so, so should I really- although I'd likely always view them with suspicion and slight anger that they hurt their partner.
I'd definitely say sexually assaulting a child shouldn't be forgiven. Rape and murder, it's hard to find justification for. As to whether good deeds for the rest of their lives can make up for that- I wouldn't like to judge but I mean- everyone used to praise Jimmy Saville for all the charity work he did. It's said he raised something like £40 million for charity. He was intrumental in raising funds for the Stoke Mandeville Hospital, where he volunteered as a porter... He also allegedly abused 60 people there. Even if you raise £40 billion for children's charities- does that really make up for assaulting just one?!! Plus- these sorts of people use this clean, good guy image as a smoke screen. And even worse- they sometimes do it to gain access to children- priests, childcare workers, teachers, nurses.
But as for the question- can people redeem themselves from their past misdemeanors? Even very serious ones? Maybe but I'd hate to be the one to have to judge because ultimately- when they get it wrong, more people could potentially be hurt by them.