I don't think there's any clear way to handle it, but I'm not afraid to explain to others why the guest list is set up the way it is. The guests can be offended or not, but inviting married/engaged/living together couples vs. only inviting one half of a not married/not engaged/not living together couple is an acceptable practice. Sorry, but when you're working on a budget, the line has to be drawn somewhere.
The OP's hypothetical situation has an engagement occurring after the invites go out. The offended now-invited guest might need an explanation on the social rule of inviting both halves of a serious couple. If the now-invited guest were still offended, I wouldn't worry about it as it wasn't intended to be a snub. That guest could opt not to attend.
For my own guest list, we learned a couple broke up just before sending our save-the-dates (DF's cousin and his live-in GF) so the save-the-date was addressed only to him. If he should be back together with her seriously prior to the invites going out, we'll probably invite her with him (we've met her). If not, he gets an invite just for him and no +1. However, should they get back together seriously before our wedding but after sending the invites, we'll probably include her. If he were to get together with anyone else? Then, no. I already omitted about 20 of my relatives, and DF left off a few people who mean a lot to him -- all of these people were left off the guest list because we can't afford to invite them so we're not inviting people we don't know. If anyone were to make a stink about it, I'd point out that it's OUR guest list (and, again, I can play the card where I omitted 20 relatives on my mother's side and included zero relatives on my father's side -- we're talking about leaving off about 75-100 relatives who are first cousins and biological aunts and uncles so I don't think anyone else's argument would get very far with me).