Does that have any effects back in country A?

Yes, you lose all the rights you have as a citizen. That means you’ll need a passport and/or visa to visit if one is required, you can’t live there anymore without a formal agreement like a work visa, you don’t get any health insurance offered, you can’t get government assistance, you can’t vote, you can’t own firearms if that’s allowed, and any other rights that citizens in your home country have. You are no longer a citizen.