I am just saying that the attitude that family members should be concerned about being a burden has another side to it. Some people do not look at it in that light, and, with the right help and support from society, should have no need to. I know that in many cases that support is not forthcoming, but we cannot endorse a situation where the definition of being a burden depends on the state of how we as a society support those in trouble.
I spent 25 years working with people with disabilities, mainly young people. Our job was to make their lives as happy and productive as we could. We certainly did not start from the assumption that they were a burden, but from the position that every life is valuable and worthwhile, and that our job was to foster that and bring out their talents and interests. I do not see it as being any different with elderly people.
Clearly it is an individual decision as to whether someone feels that their life is worthwhile; but it would be wrong to be forced to base that decision on a fear of being a burden to others. By all means a decision on the basis that they are in pain or extreme discomfort or that, despite the best efforts of our welfare and other services, they feel that life holds nothing for them - but not on the basis of thinking they might be a burden.
It reminds me of the movement in the 60s that said that there are no disabled people only disabling environments.
If our society regards those who cannot look after themselves as a burden, rather than as valuable human beings, then people will be influenced to feel that their life should be ended.