Now that she is an overstayer I would think that there would be a period that she would be denied any kind of visa if her visa was stamped in such a way. I don't know about Cyprus, but in the UK I think it's about 3 years.
You could look at crossing to the Turkish part and leaving from there I suppose, though I don't even pretend to know the ins and outs of doing this, or if it's even possible to do this.
Iain.