The friend who offers a specific practical visit can make independence easier to keep.

Vague offers put the work back on the person who needs help. Let me know if you need anything requires them to identify a task, judge whether it is too much to ask, and then ask, which is often more effort than doing it badly alone. Naming a specific thing removes all three steps. It also keeps the exchange ordinary rather than turning it into a request for rescue, which is most of what makes help acceptable.

Pick one person and offer something exact this week. Tuesday evening, the bins and the shopping, half an hour. Small, dated, and easy to say yes to.