Most people can shop for coverage in the Marketplace. To be eligible you must live in the state where your Marketplace is, you must be a citizen of the U.S. or be lawfully present in the U.S., and you must not currently be incarcerated.
Not everybody who is eligible to purchase coverage in the Marketplace will be eligible for subsidies, however. To qualify for subsidies people must not be eligible for certain other types of coverage, such as Medicare, Medicaid, or an affordable employer plan. (45 C.F.R. § 155.305; 26 U.S.C. § 36B(c).)