This was already discussed ad nauseum in the thread about it.
The bill covers those who would have qualified for the stimulus and unemployment benefits had they been citizens.
The argument for "illegals" is tied to the natural flow of people and capital that has been a mainstay of all modern economies for centuries now, and that there is a required amount of labor. Losing your job during an international pandemic doesn't mean you can suddenly re-uproot yourself with ease, and leave the country.
For those who are renting (which are the vast majority), and paying bills and debts, this also acts as a subsidy to the landlords, local businesses, and debtholders.