No chance US would allow this to happen.
You may or may not know, when renouncing US citizenship, you may be paying exit tax. The filing fees themselves are pretty high. A lot of the times at the interview in foreign embassy (that's where US citizens renounce), US officials ask multiple times if one is renouncing voluntarily and whether they are 100% sure.
I guess tax liability on worldwide income is one of the reasons US doesn't have laws about automatic loss of citizenship by simply living outside for too long.
I'm not aware of automatic loss when acquiring foreign citizenship by US citizen either. The other country may ask US citizen to renounce citizenship as a prerequisite for granting them their citizenship though.