Can the check digit come out as 0 or 1?
No. Since the check digit is always 98 minus a remainder from division by 97, and that remainder ranges from 0 to 96, the result stays between 2 and 98. A CNJ number with DD equal to 00 or 01 is already formally wrong, without even finishing the calculation.
Can two cases share the same NNNNNNN?
Yes, and it is common: NNNNNNN alone does not identify the case, only the full combination with year, segment, court and origin does that. That is why the check digit calculation includes those other 4 fields, not just the sequential number.
Does a correct check digit guarantee the case actually exists?
No. The check digit only proves the 20 digits are internally consistent with each other, a math check against typos. Confirming the case actually exists and is active requires querying the court or a database like DataJud, which pulls data straight from the courts' own systems.