I guess that if you "overstay" in the EU then you simply won't be covered, with all the problems that brings if you have an accident/need to claim etc (and it's illegal, to boot!).As the Ukraine isn't in the EU , your EU insurance is irrelevant and you'll need Ukraine insurance (bought at the border, in my experience of Non-EU Balkan-type insurances).You shouldn't be asked for Proof of Insurance on leaving the EU, but if Polish police do a spot-check and find you're not insured then expect a roasting...
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