I would train an elderly client much like I train my other clients. Using their goals, strengths, weaknesses and areas of concern as a guide. Then using regular assessments and progressions as a guide. Check in regularly to see how things are going and ask questions to see how they feel about the program, how they feel during the workout and how they feel afterward. I always ask clients if they think their homework is achievable. If it is, we go for it! If not, then I ask more questions and see what we need to tweak to make it so.
You’ve received lots of great advice and I’m sure both you and your client will do great!