Not always true. My felony convictions certainly didn't mean poverty for me. I made a damned good living for most of 40+ years...while being a felon. Sure, I worked construction, not in an office somewhere, but I still made $30-$40/hr...with a load of overtime and some of the best health & welfare benefits (medical, dental, optical, pension, etc) in the building trades on the west coast. For many, many years, the only time I was out of work was when I WANTED some time off...in my 30 years working construction, my felony record only kept me from one job...working in a very sensitive area at Lawrence Livermore Labs...everyone had to pass a strict FBI background check. Even though my felonies at the time were more than 30 years old...I failed the background check. (and I was fairly certain I would when I found out that I had to undergo said test)
At will GENERALLY means just that. The employer can fire the employee for any reason that's not illegal under state/federal law.(discrimination, etc.) and the employee can quit at any time for any reason...and is not required to give notice when doing so. (unless you have a contract that requires notice)
OP, if you lied about your criminal background, that's usually cause for immediate termination...and depending on state law, can be reason to deny you unemployment benefits. If they never asked...and you didn't disclose your "history," then, depending on company policy...and the type of job you have, you MIGHT be OK. Obviously, if your convictions are for some form of theft...and you hold a job that requires you to handle cash...you may have a problem...same if your convictions are for DUI and you have to drive a company vehicle as part of your normal routine...but that SHOULD have been caught a LONG time ago.