Are there instances where a nation does trade with another nation just to acquire their currency without much of a need for their products/services?

Is there ever a circumstance where a nation needs USDs and will engage in unfavorable trades with the USA just to acquire dollars?

Are there instances where a nation does trade with another nation just to acquire their currency without much of a need for their products/services?

For example, could a nation sell a lot their goods/service at a steep discount or even a loss just to acquire USDs?