I've interviewed people for jobs that involve felonies and I didn't automatically chuck the resume. I heard them out. Now, there are some crimes that I imagine you can't ever shed. B&E or most types of theft fall into that category. I'm not saying impossible, but people aren't going to willingly trust their money to people who have proven untrustworthy - and if it's a felony type of theft, it means that it's a large amount.
If someone committed a rather bad crime, they could get out and work at...oh, let's say McDonalds. Put them on a drawer, which is a money trust job (very small amount, but still....baby steps). If they work there long enough and always get drawers closed out with proper numbers, they can be put in charge of better things.
The real problem exists when you're being stacked against a pile of resumes with people who have NOT committed felonies. Would you hire someone coming out of high school for an accounting job when someone with a BA in accounting has applied, just because you feel sorry for them or "want to give them a chance"? Nope.