Just because someone has been forced to immigrate to the United States illegally, due to the horrible conditions of their home country and the nightmare of American immigration laws, does not mean they should be penalized by being prevented from living here. The vast majority of illegals should be granted citizenship in any case.
In theory it of course is good for all people to have homes or apartments. But the landlord would need to be sure that the renter would not flee without paying, as would surely a mortgage company. So it is not really feasible that the illegal immigrant would be invited to purchase or rent housing.