There are many things that could support elders and make it more possible for them to make contributions to their communities. Let us examine a few of them.
Health. As you imply, the physical and mental health of the elderly is very important to their ability to make a difference in the community. An elder who has lost their faculties is not going to have many (if any) ways to help their community. An elder who is sick or who cannot walk well will at least be able to help in some ways. They will be able to give advice and emotional support to younger people in their families. Depending on their condition, they can still do things like tutoring kids who need help with school. There are certainly more options open to them if they are healthy.
Finances. This is the other one you mentioned yourself, though it is perhaps not as important as health. An elder who lacks money will still have the time to be of help to others. At the same time, however, they will probably need help themselves from groups that provide things like food for elderly who are in poverty.
Skills and education. An elder who has more education and more skills can typically do more things for the community. For example, an elder who was a teacher will be able to tutor children who need help. An elder who was a business person can give advice to people starting their own businesses. The more things an elder knows how to do, the better they can help their community.
Connections to those who need help. If an elder does not know how to get in touch with those needing help, they will have a much harder time helping anyone. If an elderly retired teacher wants to help by tutoring kids, it will be very helpful if there are schools that have programs in which the elderly can help. If those programs are publicized, it will be easier for the elders to help. In other words, there need to be systems in place to connect the elderly to people who can benefit from their help.
Transportation. It may be that some elderly people are no longer able to drive or perhaps to afford a car. Therefore, it becomes important to have ways to get them from place to place. If there is good public transit, or good low-cost taxi-type services, the elderly will be able to get to the places where they can be of help to their community.
These are a few of the types of factors that will help elderly people be of service to their community.