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Both "Rude" and "Martyr" really symbolize how the protagonist is and ends up respectively.
"It carried them to their door, Rue [street] de [of] Martyrs [one who suffers], and they slowly and sadly entered their small apartments."
They will in fact suffer as a result of the necklace's loss.
Rue simply means street hence "street of martyrs". I always thought there was something to the rude thing and the character of Mathilde Loisel but I'm not sure how academic that is. Still she does consider herself a martyr by how she ends up.