、。
She took advantage of our hospitality, paying not a single sen, and stayed a full month.
Literal
She [topic-は] our hospitality [object-を] taking-advantage-of, one-sen-even pay-without full one-month stayed.
Three constructions in one. ~をいいことに ('taking advantage of ~') has a faintly accusatory edge — the speaker disapproves of the exploitation. 一銭も払わずに literally 'without paying even a single sen' — 一銭 is a long-obsolete coin (one-hundredth of a yen, abolished in 1953), kept alive in idiomatic phrases like 一銭の~ない to mean 'not a penny.' The connector ~ずに is the literary equivalent of ~ないで ('without doing'), more common in writing than in speech. And 丸一ヶ月 ('a full month') uses the prefix 丸 ('whole, complete') to underline the duration. The sum is a vivid mini-narrative of social abuse.