if a state taxes the S-corp at the S-corp level it may allow you to carry back the loss or it may only allow a carryforward or deny any c/b or c/f. at the individual level you report the loss on your return then if you have an NOl (you may not even if a business has an NOL) currently you can make an election to forgo the carryback on a timely filed return. if you don't make the election or fail to timely file the election (due with timely filed return including extensions) it has to be carried back to 2015 (2020 NOL) and then forward.
how can you have a business NOL but no NOL to c/f or c/b
say $10,000 in business losses, $22,400 in non business income, and std deduction of $12,400. taxable income (line 15) is 0. your business losses of $10,000 must be reduced by the excess of nonbusiness income ($22,400) over non-business deductions (the std deduction of $12,400) or a net $10,000. thus your NOL is $0. put another way. you usually won't have an NOL if adjusted gross income is positive.
for more info see form 1045 schedule a and the instructions
https://www.irs.gov/pub/irs-pdf/f1045.pdf
https://www.irs.gov/pub/irs-pdf/i1045.pdf
