The Wikipedia page on resignation states the following:
Although government officials may tender their resignations, they are not always accepted. This could be a gesture of confidence in the official, as with US President George W. Bush's refusal of his Secretary of Defense Donald Rumsfeld's twice-offered resignation during the Abu Ghraib prison abuse scandal.
However, refusing a resignation can be a method of severe censure if it is followed by dismissal; Alberto Fujimori attempted to resign as President of Peru, but his resignation was refused in order that Congress could impeach him.
The implication is that a resignation can be refused (potentially leading to being fired), and that the tenderer of the resignation is stuck in their post.
Does this mean that someone who needs to resign in order to quit cannot leave their job of their own volition? If so, what is the reason for such a system (in the USA), and who (in the USA) is in such a position?