Depends where you are, I guess. In a prison-first rehabilitation-last country like USA, yes. In EU, many countries will close your criminal record after some years (7 in Estonia) at which point nobody other than law enforcement itself can see that you have a record. Not to mention that even if the crime you did was fairly recent, no company has the ability to check your background without your permission, and even then it is not something that is being done in the vast majority of places.
In other words, once you've carried out your sentence, in 99% of the cases it's done and behind you, and you can go on living a normal life without anyone else needing to know.
But if you're restarting your life after serving a sentence, if you're poor it will be very hard. If you have wealth you probably can easily put your crime behind you.
In other words, once you've carried out your sentence, in 99% of the cases it's done and behind you, and you can go on living a normal life without anyone else needing to know.