Parents own the responsibility of the sins of their children until the child has reached their age of Bar/Bat mitzvah. There is even a blessing Baruch Shepetarani the father makes which thanks Hashem for releasing them of the burdens of their child's sin.
My question is about parental responsibility and whether that burden truly gets lifted if the parents did not do their job as required. Making a baby and raising a child to be a respectable member of the community are two different things.
Is a parent truly free from the sins of their children if they were irresponsible (beyond reasonable common sense) in the way they raised them?
Is this line of adulthood (where parents lose responsibility) a hard line or does it slide depending on how poorly a person raised their child?
Can it be argued a person raised in an absurd situation, where immorality was taught as morality and vice versa, that a child cannot retain the full responsibility of the sins they were raised to believe were normal behaviors?