It depends. If your only AZ source income is a rental property in the state and the AZ part of the amount on your federal Schedule 1, line 5 is a negative number you do not have a filing requirement in AZ for this year or previous years. Your AZ Gross Income on line 26 of the AZ Form 140NR will be zero.
If the AZ amount on Schedule 1, line 5 is a positive number you may have an AZ filing requirement. For tax years 2020 and before if your AZ Adjusted Gross Income (in your case only AZ rental property part of schedule 1, line 5) is below 5,500 you do not have an AZ filing requirement in those years.
For tax years 2021 and forward if the AZ amount on Schedule 1, line 5 is a positive number you must prorate the AZ Standard deduction for your filing status by the ratio of AZ gross income to Federal Gross Income. For example your AZ gross income (S1,L5) is $4000 and your federal gross income (1040, line 9) is 50,000 then your ratio is 4000/50000 = .08
If your filing status is MFJ the standard deduction is 25,900 x .08 = 2072. So you would have an AZ filing requirement since your AZ income (4000) is above your AZ standard deduction for nonresidents (2072).
As for any passive loss limitation carryovers, those are accounted for in the Schedule 1, line 5 amount. In whatever year those losses are allowed they will be reflected in that rental income line.
The same will be true for any depreciation recapture. That will be reflected on schedule D and line 7 of the form 1040. Any AZ portion of that gain is part of AZ Gross Income that you would add to the AZ portion of Schedule 1, line 5 to arrive at your net AZ gross income. Again, if it is negative, no filing requirement, but if it is positive you must use the proration formula.
Here is the AZ reference for filing requirements and the definition of AZ Gross Income from AZ tax code ARS 43-1091.
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