The penalty is predicated on the household income, rather than the individual.
3 people live in the household, but only two have income and health insurance. The son is unemployed without health insurance. Who is not on the income statement. When they file will they be charged the penalty because of the unemployed son for not having health insurance?

Yes, because he IS a member of their household and presumably their dependent.

If he is NOT a dependent, i.e. he files his own tax return, then he may qualify for an exemption due to his low income level. If not, HE pays the penalty on HIS tax return.