If they are ill or having diseases that require doctor visit and treatment, especially infection, so uninsured people have go to ER if they couldn't afford to see a primary doctor. Remember about untreated strep throat will leading to more complication like rheumatic fever. If you are very ill other than common cold and doesn't know about what's wrong so always see doctor for check up.
If family is too poor or having a entry level job like minimum wage so they couldn't afford to insure their child. Sometime, the child from poor family will qualify for Medicaid but from lower middle class with stinky benefits, it has no chance to get a Medicaid. They will end up with numerous medical debts and drive them into bankruptcy.
They do have responsibility and if they have job with stinky benefits so they have no choice at all. Having own insurance is very expensive.
When I lived in DC, I was thrown to ER at midnight because unable to breath with extreme nervous, they found that I have pneumonia, it was extremely pain for me.