Gigatron:
If it’s in the case of the US they could always just hold a green card, as I did for years until I became a US citizen only a few days ago. Granted I’m not 100% sure how the law in Japan works with this, but I’m guessing that as long as you’re just a permanent resident of your host country, and not a citizen, you can keep your Japanese citizenship.
The same works in reverse in Japan, where if you’re a permanent resident you can keep your original citizenship, until such time as you wish to apply for Japanese citizenship, in which case you’d have to renounce it.
I’ve read that the Japanese government isn’t actually that stringent about renouncing your former citizenship after becoming a Japanese citizen. It’s definitely in the letter of the law, but I’ve heard that the Japanese government really doesn’t care that much.
Also, congratulations on becoming a US citizen!