This is a common misunderstanding.
If an American loses their job for any reason, they can always keep their current insurance through COBRA. In fact, they don't even need to take any immediate action. If they need healthcare in the month of, or month after, their loss of job, they can go get it and then later on pay their premium to have the insurance retroactively go back in time to cover them. The only difference is that the covered person needs to pay the full premium, while the standard employment agreement has the employer paying a significant portion of the premium.
For people who don't want to stay on their previous employer's plan, the loss of the job is a "qualifying event" which allows them to immediately do things like join their spouse's plan or sign up for an individual "Obamacare" plan through healthcare.gov. There are subsidies based on income to make the premiums manageable for low-income people if they can't afford the market rate.