not quite. woo hyung is still employed but suspended from his position for most of the story. there was the initial hit to his reputation/work social life ("how could a police officer get captured and raped like that? you're supposed to be strong and smart and manly enough that that's never a possibility for you!"). that sense of shame and trauma he was going through made him act up to the point that he got suspended from his job. (see ch. 5)
then there is a stigma against mental illness pretty much everywhere, which is codified in policy for woo hyung's position that officers can't have a mental health record - so getting actual psychological/therapeutic treatment for his trauma would make him ineligible for the job he had been working towards. that's why he pursues sexual relationships with sujo and boguk the way he does, as a homebrew "treatment" for his trauma.
Did they really fire him from the job because he was raped?... I hope this is an overdramatization and this is not what happens in that country