Is person responsible for his incapable sibling?

you have no automatic responsibility for anyone that you are related to who is an adult. the responsibility of your relative's well-being lies solely with your relative, not with society, and not with you. any help that you give them is your decision to be made according to how much you value them and/or the circumstances of their incapacity (temporary, accidental, or otherwise).

The answer depends on what you want. Once you decide which way you want it to go, you take responsibility for the outcome. If you are willing to help a little but not take on a life time of responsibility, you may offer support for a fixed period of time, with hard rules and a hard date of final separation. The two of you can set agreed upon requirements for continued support, becoming less and less as that person becomes more responsible for themselves. You must be willing to accept the consequences of failure long term, ie; their imprisonment or homelessness. You can not blame yourself if that person refuses to follow the rules leading to living a responsible life. Not all eaglets happily leave the nest and sore into the sky. Some die. Some, you may give a second chance ... catch and coax and try to motivate but sooner or later it is up to the individual to decide are they willing to work hard at the job of living this life or fall to the rocks below. .

What responsibility does a parent have to an adult child with the same problems?

The person you describe is not incapable. One would not have such a responsibility to such a person. One would, indeed, have such a responsibility to an incapable sibling. Now, I have a question for you. Are you a real philosopher, or do you just play one on the internet? The (real) philosophers I know are much more adept with language.