Yes Renaud, if someone resigns of own original citizenship or is taken it away, is only under the rules of his new citizenship's country. If someone has two (or more) citizenships, it depends on the deals between two (or more) countries - which is the most frequent case, because of course there is a problem of the taxes AND military service. I have private international law next semester, so that's all that I can tell you
But I think without a deal two countries (assuming someone has two citizenships) can call a person to pay the taxes. This is what used to happen to Polish workers in UK. Now the countries cleared it, and there's no problem anymore
. For a tennis player there is also another problem as he must pay a tax from the prizes in the countries where he earned it. It all depends on the dual deals like I said, if someone has to pay a double tax.
The different situation is when you register a commercial law's company in a tax-free zone. The company doesn't pay a tax, but the people who make it have their personal incomes and have to stick to their national statio fisci
This is a big abbreviation what I said, because people of course find a million of holes to avoid high taxes, then every case should be considered separately - I only gave a general rule