Anash,
I would talk to those students who never do any homework and try to see what is going on. Annette is right, many of them will be the ones who are at school early and someone in the cafeteria (or wherever they go) can sign off. I also allow students to have a sibling do that. Another thing I do is allow students to stay/hang around after school. They can do HW or at least the part where they would need others or have someone check. Sometimes I will allow another students to check it and sign off or sometimes I will even do it. There are many ways to work with those students. Also, you could differentiate your HW in another way within the one, two, three stars. Give them something different for a one, two, or 3 star. They will know if they have done it and that will earn them their points for HW. Do you have to submit a HW grade on the report card? If not, I would not attach a grade to it, but that's just me. I see HW as practice that will help them do better and will effect their grades in the subject areas because of the practice they do with the HW. That is how the HW plays into their grades.
I would suggest that you don't count your students out of being able to do the homework, regardless of their home life, because it is good practice since they will have to do homework in the years to come. It also helps them to practice being responsible. But, YOU are the expert on your community, your students, and your classroom, so do what you need to do and what you feel is right. As students show growth in completing hw and doing a certain # of days in a row, definitely award super improvers stickers for that! Personally, for 1 star, its reading 20 min, 2 star is spelling hw, 3 star is math. They all must have their agenda signed. And I teach in the 13th most poverty stricken community in the US and all but 1 or 2 get it all done each day. (I provide them with help, a safe place, and options to help get it done.) Good luck adjusting the HW model to fit your needs. Let us know what you decide! : )