Let's say I become a citizen of a country that doesn't allow dual citizenship. During naturalization, new country B tells me I have to renounce citizenship from old country A.
Does that have any effects back in country A? How would country A know? Would country A even care if they found out?
Yeah, being stateless is really bad. There's a few international agreements to avoid the creation of more stateless people, but it still happens. You end up with people spending years in airports or jails as their visa expires and they have no way to renew it or get a visa for elsewhere, and asylum claims can take months to years to process, and get denied anyway.
No, other way around. Most countries won't even allow you to renounce if you don't have another citizenship.
The US also charges $10,000 dollars to accept your renunciation. The US is one of the few countries that taxes its citizens in foreign countries so there's a big incentive to renounce when you get citizenship in a better place. There is a substantial tax deduction for the first ~150K you earn in another country, as long as you spend less than 10 days in America or traveling and pay taxes in that country, as long as that country has such an agreement with the US.
Most countries tell you to renounce after you gain the new so it isn't a problem. A few allos dual citizenhip. (maybe most allow dual? I seem to recall that but it is outside where I'm sure)
It's very difficult to enforce. I've heard of cases where people like show the embassy a passport of a citizenship they said they renounced by accident, and were just sternly told to renounce it, other cases where their new citizenship was revoked.
Countries typically don't allow that. (Do any allow it?) For example, Canada requires you (at least) to be a citizen of another country and to live outside Canada.
The UN would likely consider it a violation of their human rights if a country knowingly allowed a citizen to become stateless. I would hope that at least all member states would not allow it, but I don't know for certain.