Upvote:2
First, don't overstay. It's against the law, so you just shouldn't do it. Consequences may vary, but I can offer a similar story.
A relative of mine was was a student in Hungary and overstayed his visa.
Upon exit, the border control officer notified him that:
The immediate outcome was loss of a flight ticket (he intended to leave Hungary by air, but first made a short trip across the border, which became one way).
He did pay the fine, and had no problem traveling later, including Hungary (some years later).
I think it's likely that overstaying in Cyprus would end up similarly - you'd need to pay a fine, and will have trouble traveling otherwise.
If course nobody promises such an outcome. You may have trouble even if you do pay. You may be detained at the border instead of being sent out.