I find it useful to think of two types of forgiveness.
The first is the type where the transgressors acknowledges what they did wrong; apologises, makes amends and asks for forgiveness. That’s the type of forgiveness where it’s possible (although not in any way guaranteed) that there might be some kind of relationship going forward. That depends on what was done, how sincere the transgressors is, whether they really change, whether they add anything to your life.
The second can be expressed as “Forgiveness is giving up hope for a better past”. It’s is a narrower in scope. It’s more like acceptance. Not of the person, but that what happened happened and can’t be changed.
It based in the idea that being angry with someone is useful when it can lead to change, either in you, in the relationship or possibly in them. But when there is no hope of change, when there is no future to the relationship anger is pointless and unresolved anger can be toxic to the person who feels it. “Holding into anger is like drinking poison and expecting it to hurt someone else””. It’s a frustrated hope for change that will never come.
So you use the anger that you feel as emotional fuel to give you the strength to take that person out of your life as far as you can, to make you wiser and less likely to get into that type of situation in the future. It’s almost like you let it cauterise a wound.
And the act of doing that uses up ithe anger in a useful way, lets you leave that anger behind and move on. And it is better for you if you can do that.
So it’s forgiveness in the sense of forgiving a debt. You give up all hope of getting that money back. But it also means you won’t ever lend that person money again. It doesn’t mean you have to see them as a good person, or let them back in your life. You can be wary of them and people like them.