Why do you think there is a specific word for such a person?

Thank you for your attention.actually it's an adjective for these kind of families I mean the families that have this kind of head of household

My first thought was deadbeat or a deadbeat dad. if he is in prison and won't financially support his kid. It's a slang term though. and kind of derogatory. I don't think there's a formal word for it, but I think irresponsible would fit best.

Perhaps that he is 'unfit' to be the head of the household?

Is it mismanaged????