Your specifications of the system start go get confusing near the end of your answer and in the comments since you define both the conductor and charged object as "objects". So Let's first define our system more carefully.
Let's say you have a neutral conductor and an insulator with a net positive charge (say some fur after we rub it against rubber). Now we bring the insulator close to the conductor. There will be a net movement of free electrons in the conductor to the side of the conductor closest to the positively charged fur. Thus the conductor will become polarized with a net negative charge on one side and a net positive charge on the other side. The conductor is still neutral.
Then let's say we ground the conductor (by touching it, perhaps). Then this allows more electrons to flow into the conductor, giving the conductor a net negative charge. If we then remove the grounding from the conductor without moving the fur, we will then be left with a conductor with a net negative charge since it gained more negative charge through the grounding process.
Now, you seem to be confused about how the conductor maintains a grounded ($0$) potential even though it has a net negative charge. You have to consider the entire system. When you ground the conductor, the charges then more because of the positively charged fur. The final configuration of charges will be one where the potential on the conductor is $0$ in the presence of the fur. This might be more clear if we look at two scenarios
- Instead of removing the grounding we take the fur away. The conductor will become more and more neutral as the fur is moved farther away, and the entire time it maintains a $0$ potential. This is because it is grounded, so the charges will rearrange themselves in such a way to make this the case.
- At the end of the above scenario we move our fur away from the negatively charged conductor. The conductor will now be at a different potential (relative to the ground it had been hooked up to originally). This is because you moved the positive fur away, but the negative charge is not able to leave the conductor.
In any case, the issue you most likely are facing is not taking the entire system into consideration.