The effectiveness of social insurance programs

We know that the effectiveness of social insurance programs for individuals facing adverse events like unemployment, depends on the level of self-insurance available to them. Now, think of the stimulus check that was given by the federal government to people this year due to the pandemic. Were there any income restrictions on the check? If yes, why? (Try to motivate your answer from the point of view of the government, and thinking of self-insurance versus social insurance. Write in your own words.