Depending on what level of exam the person just passed. During the Song dynasty, around 1000 AD, there were three levels of examinations. Regional, provincial, and court. Also there are martial and arts, depending on what exam you participated the results differ. If you rank at the very top, you'd be invited to participate the court exam under the direct supervision of the emperor himself. Passing the court exam can make someone over night from poor peasant to prime minister. Lower rankings might get you some employment opportunities at local bureaucracies. After the emperor Yingzong's (1065AD onward) reforms of the examination system, all exam participants who passed court exam would be issued government positions, regardless of ranking.

As far as Song dynasty's exams are concerns, it is very meritocratic. Several improvements were made to ensure fairness also traveling and food stipends were handed out to traveling and poor exam participants. The emperor Yingzong also issued decrees such as double blinded exams, the exam taker doesn't know who the marker is and the marker can't see the name of the exam taker because the name is sealed. So the exam taker can't find the right person to bribe, and exam marker can't abuse their position through nepotism.

Total amount of people passed the exams during the Song dynasty was around 40k out of an adult male population of more than ten million. So the competition is fierce. If you have reached that level of scholarly prowess, opportunities will most likely to find you without your worries.

I didn't wanted to specify a time period for fear that the question may be too specific. If it's a concern, we can fix around 1000 AD.

As a sort of follow up, how likely was someone from a poor background to have the opportunity to take or pass the exam? Was literacy preventative enough, or was an at least "middle class" (to use a perhaps anachronistic term) background a prerequisite?

Even if that were the case I imagine OP's general question would still apply regarding the treatment differences of the nobility/wealthy and less advantaged exam takers. But I would be curious to know the extent to which imperial exams were feasible to much of the population.