I believe I already mentioned, banks, creditors and services like utilities understand the furloughed employees will be getting paid for the time they didn't work once the shutdown ends. They also have other incomes in the household, savings, retirement loans, and leave they can sell back to pay the bills.
I just got a text from HECO that supports my comment. Anyone suffering a hardship due to the shutdown can contact the company for alternative options.
They have available no interest payment options where they roll up all your missed payments and spread them out over 6 months. Once you get your backpay, you can either pay off the missed payments and resume your normal monthly billing, or you can pay over the time period they offer you that normal monthly payment plus 1/6th of the outstanding amount without interest or late fees.
That's just one example of how a gov't shutdown might be an inconvenience for those living paycheck-to-paycheck, but everyone knows you'll get paid eventually and most are willing to provide accommodations.