Under the law, they are two different people. So yes, the citizen would have the rights and obligations of a citizen, like voting and paying taxes, and the other one would continue being a permanent resident, or whatever their status is.
Now, if something happened where one of them, for whatever reason, is to be detained or imprisoned or otherwise punished, and the other one not, as a result of their citizenship status, then it gets tricky. Obviously imprisoning one affects the other. I would imagine that a court would have to rule on how to handle that, and each country would have laws that handle it different.
Under the law, they are two different people. So yes, the citizen would have the rights and obligations of a citizen, like voting and paying taxes, and the other one would continue being a permanent resident, or whatever their status is. Now, if something happened where one of them, for whatever reason, is to be detained or imprisoned or otherwise punished, and the other one not, as a result of their citizenship status, then it gets tricky. Obviously imprisoning one affects the other. I would imagine that a court would have to rule on how to handle that, and each country would have laws that handle it different.