The problem with the sentence is with the usage of present/past tense. If Mary had not attended the meeting (past tense), she would never meet (present tense) her old friends whom she had not seen in years. The sentence should read " If Mary had not attended the meeting (past tense), she would never have met (past tense) her old friends whom she had not seen in years

While Steven is correct in changing 'would never meet' to 'would never have met', it is not the past tense, but the third conditional, used for hypothetical or unreal situations. https://www.englishclub.com/grammar/verbs-conditional_4.htm