Yes, they check previous employment.
I also want to share a somewhat different viewpoint, one that you might not get here.
The state of law enforcement in this country has declined. A lot of contemporary law enforcement does not mean being part of the solution, but rather part of the problem. Much has changed because common sense has been exchanged for unethical behavior.
Consensual activity is disdained by law enforcement. It is considered a crime when two adults making a marijuana transaction, even though both parties mutually agree to the transaction.
Asset forfeiture is seizing the property of people who are assumed guilty and have to prove their innocence. Seized monies by police have skyrocketed in the past few decades. Citizens often lack the resources to combat this abusive practice, so police know there is a good chance of departments keeping seized items.
Law enforcement has become militarized. The acquired vehicles are not free, as some believe. The receiving police departments must retrieve the vehicles. Other costs include storage, insurance, maintenance, fuel, training, etc. These costs are not insignificant.
Police exercise wide discretion, which is contrary to what some believe. Law enforcement recently "cracked down" on people reselling NFL post-season tickets. This, again, represents another waste on citizens involved in consensual activity.
Special Weapons & Tactics (SWAT) was once reserved for hostage situations. SWAT is now used for simple matters like marihuana.
Many types of enforcement are ineffective. Checkpoints (roadblocks) are a prime example. Research convincingly shows that roadblocks are ineffective compared to saturation patrols for apprehending drunks. The same research indicates that drunk driving is not deterred by roadblocks. Law enforcement is lazily interacting with law-abiding citizens at roadblocks. INTERNAL Border Patrol checkpoints are also ineffective AWAY from the border.
There is much unethical behavior, which is sometimes called "thuggish" behavior. It is being exposed because the average person can now address it through new technology, such as cellular phone filming, You Tube, internet forums, live streaming, etc. A disturbing instance is the brutal officer who cold bloodedly murdered homeless man Kelley Thomas. You can see the cop bait Thomas in the dashcam video. The cop yells to Thomas, "[these hands] are about to fvck you up!" He fvcked up Thomas to the point of murdering him.
There are multiple websites today listing SYSTEMIC police abuse, and not just individual abuse (see comments below).