This Ship Is Sinking. Can I Jump to a Client's?

A job seeker in a senior position at a struggling marketing agency seeks advice on whether it is ethical to apply for jobs with the agency’s current clients. The agency is experiencing financial difficulties, with reduced hours and pay for employees. The job seeker is considering applying to openings with clients because of their familiarity with the players and the quality of their work. However, they are worried about exacerbating their employer’s downfall by leaving for a client. They seek clarification on whether clients would perceive this as a red flag.