It really depends on how one defines forgiveness as well as what was done and how necessary that person is to your life.
What is (your) motive for forgiveness?
Personally speaking I define "forgiveness" as "letting go and moving". It's a decision one makes to no longer dwell on an issue anymore. You can't move on if you're obsessed with something.
It doesn't mean I have to maintain a relationship with them or pretend like it never happen. To forget is to throw away a valuable lesson. It's important to remember untrustworthy people.
"Never love anyone who treats you like you're ordinary."
- Oscar Wilde
Clearly if someone is not asking for forgiveness it's because they don't feel they did anything wrong or they don't think you're all that special. The risk of losing you from their life isn't worth the effort to ask you for forgiveness! Essentially they take you for granted.