You can just ask them. Although it's very possible that they don't entirely know what they want, this isn't the kind of situation that happens with people who are good at interacting with coworkers. It definitely doesn't seem like they have some sort of endgame. If they're still approaching you to talk to you, that's a pretty good sign--that seems to me like they want things to go back to the way they were?

I'm a pretty honest person and in my experience, the best thing might be to send them a straightforward e-mail or text message out of work, more or less describing what your viewpoint is and putting the onus on them to clarify what they want you to do. e.g.-- You understand that they were upset by something you said, you think they were valid to be upset by the topic, you are sorry that this happened and have made a mental note and will avoid it happening again. You respect them as a person and have heard that they have been telling people that they feel unsafe around you, and even the sight of you makes them feel upset. You take things like this very seriously so you have been doing your best to not make them feel that way by staying out of their sight, because you care about their feelings and want them to feel safe. You want to follow their lead and avoid making assumptions about what they want from you, so please let you know if/when they would like the current situation to change, because until they say otherwise you will continue giving them space?