Active Duty will continue to get paid by nearly every bank. Does he have USAA, Navy Fed, or another bank that caters specifically to the military community? If so, he'll be fine. In each of the 3 gov shutdowns since the turn of the century (including the longest ever - 34 days - in 2018), these banks have continued to pay their active duty members because they know they will get backpay from the government.
For federal civilian employees, the final paycheck will be 10 Oct to cover the pay period through 30 Sep. This sucks, but the good news is that it is codified in law (Government Employee Fair Treatment Act of 2019) for all furloughed civilian employees to be paid retroactively once an appropriation is approved.