You have to be the detective in this situation and understand the how and why. Is this a need? If so that needs to be addressed with the school and family, there are lots of options for helping needy students, if you are willing to go the extra mile. 

If you see this as a result of their disabilities then you need to find an alternative way of reinforcing the social norms of sharing or not sharing food. Kids share in the cafeteria all the time, the question is , are your students simply participating in this? Are they mimicing other students behaviors but not understanding the social cues and therefore not participating normally? Is the asking behavior a part of their disability?

I think it is important (though a big job for you) to fully understand their situations and deal with it accordingly. If they are truly needy you will need to work with them about how and when and who to ask for something they NEED but also when and where it is inappropriate. It is hard to know if this is a case of needing to learn social norms or needing to deal with a hardship.

I think it depends on the situation.  If they know the other students, I would say it's typical high school behavior to ask a friend to share.  If they don't know the student, I would certainly discourage asking for food.  One question to consider might be why they are asking for food.  Are they hungry because there is too long between breakfast and lunch?  Are they hungry because they aren't getting enough to eat at home?  Are they asking because they really need something to eat or are they asking because they do not understand that it can be rude to ask?  I know I had a few students who would always ask for food and usually it was because they didn't have enough to eat at home.  I had other students who would ask for food just to see if I would give it to them.  

I wouldn't want to guess how much money I've spent buying kids lunches over the years. As for asking other students, that might be something to be avoided, but as others have said, I don't see where it's all that big a deal. If you are trying to teach social skills, you certainly would want to emphasize that one doesn't ask strangers for food, but if they are not strangers, I don't see where it's a major problem.

I really don't see any harm with them asking.  A classmate is part of their social group, and if you need something you ask.  Now if you were taking the kids on a field trip and they were asking random people for food I might could see the problem.

I would discourage the students asking for food; I would also consider the types of disabilities these individuals have. Are the students capable of understanding the directions forbidding them from asking for food? Do the requests for food come in response to discussions about eating, science projects involving growing potatoes, just before lunch (they do have a long morning in between breakfast and lunch), or are the requests completely random with no obvious trigger event?

I occasionally provide food for poor students who obviously don't have the financial means for snacks, but in doing so, I find that other students who have these resources try to take advantage of my good nature by begging as well. It's best to let the kids know that the teacher is not a food service and also explain that it is unmannerly and in bad taste to beg for food. Then again, many students are quick to share food from the cafeteria or from home which they don't want to eat, and I don't see anything wrong with this. I did have a student with an eating disorder who begged food from EVERYONE, and whose parents forbid her from accepting any food other than what they sent from home. Even the cafeteria workers knew not to sell her anything despite her pleas. I made the mistake of giving her some food one day before I was told that it was a no-no and that it could actually compromise her health.

Are the other students really strangers?  To me, that's the major issue.  I don't think that they're really going to see those people who are, in a sense, their colleagues, as strangers.  I don't see it as a big deal.  I think you should emphasize to them about not asking true strangers for stuff (for safety reasons) but outside of that, I don't think it's a big deal.

I personally say "always a no no."  Obviously, it becomes impossible to control what high schoolers do at every minute of the day, but as a mother of young children, I would want teachers to be echoing MY lessonsnotto ask others for food.  In your case, it seems more (or less really) is going on at home and these kids are hungry. 

I never offer students food, and discourage them from asking.  It sets a bad precedent in the classroom for what could later be construed as favoritism, not to mention the liability that could come with giving a student something he's allergic to... I don't know, the possibilities are endless and it is a door I choose not to open.

At some point, the parents need to be held accountable, but if you are providing food, or encouraging students to ask others, you are only enabling the bigger problem.