As far as her rent falling through the cracks for a year, I highly doubt it. Collecting rent isn’t something that apartment owners and managers do whenever they get around to it after making sure that everybody’s toilets don’t leak and their air conditioning works. Collecting rent is the reason they’re in business.
I think she’s looking for a sucker - someone to support her (and probably only until she finds another sucker with more money) - and she went onto OKCupid to find some lonely soul to take advantage of, using the so-called boyfriend back home as a reason to avoid having to actually have sex with whoever falls into her trap. Hell, I wouldn’t be surprised if she doesn’t wind up hitting you up for money to go visit her so-called ex to assess how she really feels about the two of you, only never to be seen again. (She wouldn’t happen to speak with a Nigerian accent by any chance, would she? :D)
Anyway, I’d lay five-to-one odds that this girl is pretty attractive, and attractive girls with the right turn of mind can play lonely guys like a violin and get them to do all sorts of things that they wouldn’t normally do. Strip clubs are full of these types of women.
They can also have all sorts of baggage, like drug problems, or friends with drug problems, or a boyfriend with drug problems, any of whom can wind up needing a place to crash for a while, and guess whose place they’ll wind up in. Then the next thing you know you’re living with a bunch of drug addicts that you can’t get rid of and worried all the time that the cops are gonna raid the place. Or she talks you into letting her male friend who is really her boyfriend move in until he gets paid or something and the next thing you know she’s banging him in your home and you get stuck with letting them stay, maybe even by dint of the threat of violence.
In other words, all kinds of bad shit that you’ve never imagined can happen when you let a vagabond move in with you, and until you know a hell of a lot more about her life (and “rent” situation) I think think the logical assumption is that a vagabond is what she is.
Disclaimer: No, I’m not speaking from personal experience. At least not of my own. But I’ve known some guys, and well…let’s just say that pretty, cold-hearted and manipulative girl + lonely guy = doormat. Broke, heartbroken doormat. Bitter doormat. Self-loathing doormat. You don’t wanna be that guy and neither does he doormat.
So in short, proceed with extreme caution. And by ‘extreme caution’, I mean “run like hell the other way”. 
No matter what her story is, too many things just don’t add up.
