Most oilfield companies will run a background, not sure if they check for warrants though. I know most companies will only look for convictions like DWI/DUI because those are the convictions that will keep them from being uninsurable as drivers on company insurance policies. But there are also TONS of jobs that don't require driving, they require you pass your initial drug test, show up & work. My BIL has had more than his share of dealings with the law, jail, prison etc but it has not prevented him from ever getting a job.
Also I've read that LL checks BL's credit report regularly, is that legal? I know when I've checked mine & my husbands there is a disclaimer that you have to check mark the box agreeing that you are the person you are requesting the credit history on, have their permission etc or something to that effect. IMO she isn't his wife & doesn't have his permission, seeing how he's not around to give it. At this point not even a bill/debt collector would talk to her regarding debts because she isn't legally his wife.
With everything we know, its evident these are not upstanding law abiding citizens, therefore IMO I'd bet the bank she has always filed single/head of household on her taxes.
With as many people the town I live in, in Odessa, that have come here to work, it would be very hard for him to be detected visually here, we've gained 30k plus new people to this area due to jobs, so he could blend in very easily. Just MOO.