You're imagining this to be more friendly than it is -- "can't pay for emergency medical care" in the US is a euphemism for "got a bill from the hospital, couldn't pay it, so the hospital sold the debt to a collections agency and wrote the account off as a loss", not a reference to a forgiveness program.

Since the hospital takes a loss in those cases (and has to, since they have to treat everyone), everyone else's cost of care goes up to subsidize the loss.