If the company isn't in dire financial straits, it's common to give some severance pay, usually tied to length of employment. This isn't a requirement.
With the US's ridiculous system of getting most health insurance through your employer, it does mean that you lose many of those health benefits. There is a legal provision called COBRA where you can continue for a time on your previous employer's health care (at your expense). The ACA (Obamacare) makes losing your health insurance less dire than it was in the past (for things like "pre-existing conditions"), but it still sucks.