Not necessarily. Parents are responsible for two parts of a child’s upbringing: nature and nurture.
One part they cannot control because it is how that person works, that is nature. By nature, I mean the temperament of the child, how well they listen, behave physically, mentally, physiologically, etc. If a child has some disability is one or several of these areas, they will not learn as easily, but that doesn’t make it the parent’s fault even though it is the parents’ genes that have created the child.
The second part, parents have more control over, that is nurture. Parents have a choice in how they raise their children such as what values you teach - honesty, respect, etc. If a child is not taught how to respect, how to be honest, how to succeed, how to lose, how to love - they will not know how to do those things. They won’t necessarily hold those values. Therefore, the parents are partially responsible for how that child was brought up.
BUT neither nature or nurture guarantees the child will be good. What determines that? The children themselves.
We are all given a choice in how we live. Some are inhibited or helped by their nature - someone is a compulsive liar or someone who is more inclined mentally to be kind to others. And some are inhibited or helped by their nurture - someone who had absent or abusive parents or someone who had loving, mindful parents. But even the people with the worst upbringing or with the worst set of genetics could be the kindest and gentlest person around while those with the best upbringing and no physical, mental, or physiological inhibitions could be a cruel, vicious person.
Now, talking about your particular hypothetical: If you have an adult child who isn’t a good person, is it the parent’s fault? Not totally, not completely. An adult child should have the ability to take responsibility for his or her own actions, albeit any nature or nurture inhibitions. It may be how they are naturally, it may be how they were brought up, BUT it may be their choice, their decision.