How can a person at fault not be liable in a car accident?

This should not happen

BUT

underage persons can not be held responsible in many jurisdictions, but their parents can.

Another View: Actually this question is unanswerable in its present form.

Rather than a generalized opinion-seeking question, the specifics of the accident would have to be known in order to answer knowledgeably.

Anyone who has been issued a motor vehicle operators license can be held "liable" for causing the accident, regardless of their age. The above answer would apply only if the at-fault individual involved was either an un-licensed minor, or was someone who had been judged mentally incompetent and ineligible to hold an operator's license.