The justice system in the US isn't really in play with people after they've done their time; when you're done you're done. However, the US civilian culture is different and the catch is that few US states' laws put any limit on discriminating against people with felony convictions, whether it be for a home today, a loan tomorrow, or a job fifty years later.
Over the past twenty years, I've been told by many folks in the US tech industry holding unskilled positions that non-white-collar convicts should never be given jobs again, should do all their time in solitary, shouldn't have books or access to entertainment, or should be beaten with stones or bats (and a few variations on this theme of torture-as-penance, always by women oddly.) Regardless of whether those attitudes are right or wrong, it's important to understand they are there and seem to be commonly held by the folks standing at the gates. And, for people who've committed felonies and done their time to understand they can either get very creative in how they adapt, or reoffend.
To bring this rambling back to the topic at hand: can "felons" get a tech job? Sure, but it's unlikely where those attitudes have had time to become invisibly entrenched, e.g., in human resources' workflow. So, as another poster said, startups are a real possibility. But really, any company where paperwork or blind-policy isn't in play--especially as a first step, e.g., a cookie-cutter job application--is a possibility. Another approach is to create the job, something almost uniquely possible in tech.
In short, it's tough, doable, and I think great because people can use it to walk far from the scenery of recidivism, figuratively and literally.