Sentence improvement — Negative fronting with subject–auxiliary inversion: refine ‘‘Not a word they spoke to the unfortunate wife about it’’ to the most idiomatic formal structure for emphasis and clarity.

Given data
Original sentence: ‘‘Not a word they spoke to the unfortunate wife about it.’’

Concept/Approach
When a negative or restrictive element (‘‘Not a word’’) is fronted, standard English requires subject–auxiliary inversion: auxiliary + subject + main verb.

Step-by-step evaluation
did they speak — Correct inversion: ‘‘Not a word did they speak ...’’they will speak — Wrong tense and no inversion; also changes time reference.they had spoken — Past perfect without context and no inversion.No improvement — Leaves the un-inverted clause.they did speak — Affirms speaking, contradicting ‘‘Not a word’’.

Verification/Alternative
Parallel: ‘‘Never have I seen such speed.’’ / ‘‘Under no circumstances will we agree.’’

Common pitfalls
Forgetting inversion after negative adverbials like ‘‘never, rarely, scarcely, not a word’’.

Final Answer
did they speak