Worn out from severe exhaustion, she quit her job and rested for a week.

Literal

She [topic-は] severe exhaustion [because of-のために] job [object-を] quit, one-week rested.

Two grammar features fold neatly together. ~のために in this sentence is the causal reading ('because of X') — distinct from the purposive reading ('for the sake of X'), which would normally take a verb-clause before のために. Here it follows a noun phrase 激しい疲労, marking it as the cause. And the bare 連用形 やめ (instead of やめて) chains clauses in a slightly more written, narrative tone — Japanese prose often prefers this stem-form linking over the spoken te-form for sequencing actions, much like how English literary writing might use comma-linked clauses where casual speech inserts 'and.'