People are not supposed to wait until they get sick and then enroll in Obamacare. Most people are enrolled during an open enrollment period. People who have a life changing event however, such as losing insurance coverage or getting married may enroll when it is not an open enrollment period. These people get to enroll in what is called a "Special Enrollment Period" (SEP).
To ensure that these people really are eligible for enrollment in a health plan, potentially including a subsidy, and not abusing the system and enrolling just when they get sick, The Centers for Medicare & Medicaid Services (CMS), which maintains the federal Health Insurance Marketplace, established rules requiring that the applicants provide supporting documentation to support their claim that they had had a "triggering event" making them eligible for a SEP enrollment.
Recently the General Accounting Office (GAO) conducted a test of the eligibility for enrollment in a health plan in an SEP, to determine if people are being properly screened. The GAO created 12 fictitious Obamacare applications. Nine of the 12 of GAO's fictitious applications were approved. Three were denied. For five of the 12, the GAO provided no supporting documentation but the Marketplace approved them anyway.
This is alarming. In 2015, 1.6 million individuals made a plan selection through an SEP. These very well may have been sick people who waited till they got sick to buy insurance. To read the GAO report follow this link.