Currency values are based on emotions of speculators. There are no rules as in physics or chemistry. There are no measures of currency quantities that determine a rise or fall.
The euro involves great debts and deficits -- some much worse than for dollars. So too for the yen, which is the currency of a nation totally devoid of resources.
Dollars have fallen because of emotions.
To stop the fall, emotions have to improve re America, or the entire world has to move towards a rational single world currency. If we imagined a single world currency, it would be massing up inside countries with a favorable trade balance. They could use their amassing quantities of money to buy things or to hoard.
That would demonstrate what happens when a nation sells more than it buys.
Right now, some speculators bid up currencies based on imagining and measuring each country's outflow and inflow. The outlook for dollars and euros is bleak, but euros rise anyway. The real mystery is the rise of euros.