I'm not sure if that would work for bitcoins acquired before moving abroad.
The law is usually clear on that for each country and it's easy to find out.
There are basically two things to consider.
1. Does the country have a tax at the end of the fiscal year even on unrealized gains? The US has it. Most EU countries don't. If the EU country we're talking about doesn't have it, nothing to pay here atm.
2. Does the country have an exit tax?
For example France used to have an "exit tax" where you had to pay something crazy like 30% of everything you had before becoming fiscal resident of another country. In that case you'd have to pay 30% of your BTC's value when you left. AFAICT the french state semi-recently suppressed that exit tax.
Other countries, more rarely, have an exit tax on unrealized gains: Spain for example. If you have spend more than x out of the last y years as a spanish fiscal resident (I think it's 10 out of the last 15 years) and then decide to leave Spain, you must pay an "exit tax", but "only" on your unrealized gains. So if you leave, you're legally supposed to pay a tax on your BTC before selling them on greener pastures.
Now to answer your question: people would need to check for the country concerned but many EU countries have no tax on unrealized gains and also no exit tax (besides Spain I don't even know if there's still any EU country with an exit tax now that France suppressed it).
So without these two taxes you're totally free to go spend, legally, 183 days a year in a EU country which has a low tax on trading / low tax on Bitcoin profits, sell your coins there, enjoy your money, and come back after x years to your home country. (the rule for fiscal residency in the EU is basically: "if you spend physically more than 183 days per year in a country you're supposed to be registered there and to be a fiscal resident of that country").
This is not just fully legal: it's what the law mandates you to do (to become fiscal resident of the country you spend more than 183 days in). It's also why when you go to "unregister" at the town hall / IRS / VAT services in your old country the public servants can be a bit inquisitive: they want to know you're really leaving and not playing games. In my case they asked for my new address. They hate it that they know they won't be able to tax you anymore.
The legal system is not "your local IRS always win no matter what". There are laws and the IRS and judges cannot overrule these laws. People are free to vote with their feet and their money.
In monopoly there's the "get out of jail free" card. In real life there's the "get out of of ultra-taxative country" card : )
P.S: Some countries shall give you fiscal residency even if you spend less than 183 days there, but it doesn't change the fact that should you spend more than 183 days in any EU country, you're supposed to be fiscal resident there. For example if you do 91 days in Andorra (which can give fiscal residency after 90 days per year instead of 183) but 200 days in France and 70 days left and right, France isn't going to fancy very much if you try to explain them that you're a fiscal resident of Andorra.