And does that mean she's starting a relationship with this other person?

It's painful either way of course, adding insult to injury that not only she broke up with you but she couldn't even be honest on the full reasons why. But I ask because her asking such a question sounds a bit strange, as if she's suggesting she might reconsider the break-up if only you'd consider an open relationship? Which is still a shitty way for her to act, but a very different situation.

I'm inclined to agree with RT that open relationships must be a lot harder than people may think, though I don't have any personal experience on the topic, and really not all that much experience with relationships in general, or at least not since a long time ago.

Edit: I'm aware these are very personal questions so feel free not to answer obviously.