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You generally do present your passport when leaving. Most places you get an exit stamp (which matches your entry stamp). They usually confirm things such as not overstaying a visa.

ex:

overstaying in Thailand results in a on-the-spot fine

China lately has exit checks when traveling to SEA (they try to intercept people traveling to scam centers)

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I have yet to leave a country (well, a state technically) without having to show a passport - with the exception of the Schengen area.
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That's mostly because transport companies have to pay to ship you back if you get turned away at the border, so they will want to see your permission to enter your destination country before you leave. I've traveled internationally a fair bit and I've never had to show my passport to government officials when leaving the US.
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I mean, really not trying to frame this in any way, but asylum seekers do it all the time.
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Ok, fair enough, but if I were German - I don't really think I would asylum anywhere on the basis of Germany maybe intending to conscript me in the future.
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I'm reasonably sure Russia would take you.
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It is quite difficult to leave a country without simultaneously entering another
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It is trivial for any country that is not land-locked. You just have to sail to international waters. What is difficult is to stay there.
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