I'm a social worker in Michigan. Medicaid has nothing to do with illnesses people may (or may not) have. Medicaid is for people with very low income and assets. In Michigan, that means an income of under $13,000 or so a year (I think) for a single person and less then $2000 in assets. Whether someone is sick with cancer, diabetes or anything else is irrelevant. I have been able to get applications "expedited" when a person is terminally ill and then the application itself is considered in about a month instead of the 2-3 months as usual. But that doesn't mean the person gets approved if they have a higher income then that.
My area doesn't have charity hospitals. Here, if a hospital system makes a diagnosis of cancer, they are ethically responsible for treating the person (otherwise it's patient abandonment). Sometimes patients don't want to stay with that system but that's all that can be done. For diabetes, hypertension, hepatitis, etc., there's free clinics in some areas where people wait for hours to see a provider.
Patients who are diagnosed with end stage renal disease or ALS get Medicare automatically without the two year waiting period for other diagnoses, including cancer. The Medicare then picks up costs of dialysis or whatever treatment. Interestingly, patients only get Medicare for two years after kidney transplant so paying for their antirejection meds after that can be difficult.
Pharmaceutical companies have "patient assistance programs" for brand name drugs that patients can get for free if their income meets each companies criterion and there's someone at the office willing to do the paperwork for each medication.
And of course we all know that having that insurance card doesn't mean that treatment will be affordable. The Medicare Part D plans vary in how much they'll cover in that donut hole. A month of Lovenox is thousands of dollars, Nexxevar also thousands. Even a copay of 20% can force a decision about stopping treatment for financial reasons. And medical bills are the leading cause of bankrupcy in this country. Oxygen can be hundreds of dollars a month for someone on anything over 4L, radiation course is often tens of thousands of dollars, TPN is a few hundred a day.
Americans can get health insurance from their employers for whatever the employer charges employees, from the government (Medicare and Medicaid as explained above), piecemeal (from free clinics, patient assistance programs, etc), the Veterans Affairs system (if eligible and with some waiting lists but provide excellent care once accessed), from individually purchased policies (which are very expensive and usually cover only catastrophic expenses and not the chronic care needs, usually not outpatient medications).
It's an amazing system we've developed here where we have the right to vote, right to high school education but healthcare is reserved for the very very poor or those who have access to employer based policies. But you asked the question out of curiosity, not in wanting to know opinions about the disgracefulness it represents.