In certain points in relationships, we may have to come to grips with "things like this might still happen". In a relationship, all we can do is tell a person what we would like from them (and why) and then it's up to them to either say "yes" or "no". If it's "no", then you are correct, we have to decide whether or not to stay in the relationship. There is, however, a third possible response other than yes or no. This is for the person to say, "Yes, I will make that change, and not just for you, but for me. I want to be different in this way as well. And, it's going to take some time for me to make this change". At this point, we still have to decide whether or not to stay. It may be that we don't want to leave the relationship and want to give them a chance to change, but we've reached a breaking point and aren't able to stay with them while they work on making the change. If they do actually do the work, then maybe we can both come back together.
The bottom line is that we all have to put our own health-mental, physical, emotional, and spiritual first. If we aren't healthy in these areas (or actively healing in these areas), we can't be in a healthy relationship, regardless of how the other person behaves, interacts, etc.