Quite a few of the people that come to see me about filing bankruptcy here at my law office in Houston, are worried about the possibility of losing their jobs if they file bankruptcy. Specifically, if their boss or employer will find out if they file bankruptcy. Like I tell my clients, unless you owe your employer money, they are not listed in the bankruptcy schedules that are filed with the Bankruptcy Court, and are not generally notified, just because you file bankruptcy.
Employers can check your credit reports, but in my experience only do that in connection with the hiring process, and they must obtain your written consent to do so. Now that being said, if you file Chapter 13, at least here in the Houston area, the Southern District of Texas, if you are a "W-2 employee" and have taxes withheld from your check, you must have your Chapter 13 plan payment deducted from your paycheck, so at least your HR department has to know about it.
So, your payroll office would have to know that you filed bankruptcy; they are the ones that are sent the "wage order" from the bankruptcy court. Don't be overly concerned about such payroll deduction or wage orders in the event that you have to file Chapter 13. If you work for a large company, many of your co-workers have all kinds of deductions coming out of their paychecks such as garnishments for child support, student loans, IRS wage levies, chapter 13 plan payments, etc.
It's likely not as big a deal as you think. If you are in a small office or you have a very responsible position, it is possible for us to ask the Bankruptcy Court to "waive" the requirement of having a wage order, but it must be unusual circumstances for the judge to consider doing it. A far higher number of Chapter 13 cases are successfully completed, if the debtor has a wage order, with the Chapter 13 plan payments being deducted from their paycheck. Moreover, employers are not allowed to fire you, or discriminate in employment against you, solely because you filed bankruptcy, or didn't pay a debt that is dischargeable (cancelable) under the U.S. Bankruptcy Code.
The only possible exception that I know to that one is, if you need a security clearance for your job. If you have such a job, of course you should inform your superiors of any change in your financial situation. I have had them investigate clients that have filed bankruptcy before, and cleared them and allowed them to continue with their classified work, so I know filing bankruptcy doesn't necessarily mean that you will lose your job, even if you need a security clearance.