Does she ask you to forgive her because she wants you back or because she regrets what she did? In the last case, she would give you the freedom to choose whether or not to forgive her, and whether or not to give her another chance (that are two seperate things, in my opinion). And both things are really up to you! Forgiveness can be good for the soul and good for relationships, even if they can't be restored, but it should be given out of your heart, of your own choice, or it can't be real. And you can only give her a new chance if she regrets what she did and if you can forgive her, or it won't work. IMHO