Well, I can tell you what I do in these situations, but I'm not going to tell you what you should do because I think you need to figure that out yourself. For context, I have had one friend come back after we had a huge fight that caused us to split and another very recent may or may not come back.

Anyhoo, here's the rules I follow for these situations:
1. Guilt or other negative emotions can't be the reason or a major one for why the relationship is being discussed again.
2. Whatever wrongs had happened to cause it to end in the first place need to be resolved, apologies need to be said and meant, and forgiveness must be given.
3. Both parties need to be willing to have open and candid discussions on how they can continue the relationship in a healthy way going forward.

Probably worth noting that with my BPD I suffer from a major fear of abandonment, so I have to be sure for my sanity that the people I allow in aren't going to leave me. Because of the fear of abandonment, I have found it very difficult to bring myself to talk to the friend who came back despite him being a much nicer person now and being welcoming. He's just not the type to seek me out, never has been, so that makes it really hard for me to approach him despite forgiving him because I'm afraid he doesn't really want me around and might leave again if I were to mess up.