I traveled to Odessa in October, 2013, for a 3 week vacation. I rented an apartment with a washing machine. I took my clothes out of the washer one day and noticed something in the bottom of the washer. I felt a sinking feeling when I saw that it was my passport! (ALWAYS!!! check your pockets!) The cheap ink that Passport Control uses for entrance and exit stamps, was of course, all washed away and my passport page for Ukraine was blank. At that point, I technically became an illegal alien, with no proof of the legality of my presence in Ukraine, subject to 'fine, exile and banishment', as Penwriter puts it. When I went to the airport to catch my flight back to the US after my vacation, I stepped up to the Passport Control kiosk and presented my passport. I explained that my passport had gone through the washer. The passport official looked at the passport; looked and me and said, “You will not be going home today!” He told me to go sit on a bench while he talked to his supervisor.
After cooling my heels on a bench for 30 minutes, the official returned with his supervisor. The supervisor invited me to come into his 'office', which was the nearest men's restroom. He shut the door and started a tirade about “This is a terrible situation”, “laws violated”, “so much paperwork to do”...I pulled out a 'Franklin' and said, “Will this help solve the problem?” Within a heartbeat I had an exit stamp in my passport and after a round of handshakes, back slapping and all around bonhomie, I headed for my airplane amid cheers of 'Bon Voyage!' and 'Schastlivovo puti!'.
This, my friends, should give you an insight into how problems are solved in Ukraine (including the 90 day visa restriction). There are some people here in positions of power and authority that recognize the contribution that expats make to the local economy, and they are willing to use their position to insure that the flow of foreign currency continues. And if some of that money comes their way, then so much the better!