How can I get new coverage?

Go to getcoveredillinois.gov and get some coverage ASAP

I'm sure what coverage you are referring to. Health insurance coverage? If so, I think the Marketplace is now open and you can view different plans and get prices, based on your current income. That's my understanding. Or you can call the Marketplace and ask for assistance in new enrollment.

Google healthcare.gov and you can explore all your healthcare options. You don't say your circumstances, but you can also visit your local health dept or dept of social services, even senior center and a social worker can help you navigate the options and also help you secure support services you might need if you have no income.