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She didn't show up at yesterday's party.
Literal
She [topic-は] yesterday [genitive-の] party [at-に] did-not-appear.
The の linking 昨日 to パーティー nudges the meaning from 'yesterday, [I went to] the party' toward 'the party that happened yesterday' — turning the time word into a modifier of the noun. Without の (昨日パーティーに...), the sentence reads as a temporal adverb sitting alongside the party rather than identifying which party. A small particle decides whether yesterday tells you when, or which.