A person can apply all they want. Just because you pay all the fees doesn’t guarantee you approval, though. There are many provisions to being approved, not the least of which are hardship cases. He needs a sponsor, and that sponsor has to make a minimum income (gross, not net), which varies per number of household members.
If the applicant has lived here illegally, in order to be approved for a green card they MUST return to the US embassy in thier country, regardless how many years they have lived here. If they don’t have a record of income tax returns, the likelihood of even being able to obtain a work permit is significantly diminished.
FYI, if either of you are on any kind of government assistence, get off of it NOW. If any member of the immediate family is on government assistence, the applicant will be rejected, and given a set amount of time to leave the country or be shipped out.