Am I entitled to any kind of money if I've been on welfare for the entire year with both my children while maintaining a residence?

No.

 The money you hear about people getting for just filing a tax return claiming kids requires you to  have some earned income (wages or self employment). Without earned income, you are not eligible for the "refundable" Earned Income Credit or Additional Child Tax Credit.

If you are a student, over age 23, and are not claimed as a dependent by someone else (e.g. your parent) you may be eligible for the up to $1000 refundable American Opportunity (tuition) Credit. That credit is not dependent on having either kids or earned income. You must be at least a half time undergraduate student and actually paid tuition (not just had it paid by grants). Tuition paid by loans counts as paid by you (since you have to pay that back, someday)

It acctually depends where you live. Canada or USA....r somewhere else? which province or state etc. For example in Ontario Canada, rent is taxable. Anyone paying rent....gets a small percent back. Even if your on welfare. But in most provinces in canada rent is not taxable. So one would need more information from you before being able to accurately answer your question. The internet is a vast space consisting of billions of people around the world. Nobody could possibly know how to answer that question without knowing anything about your situation....

Well his username is MarkinHawaii so I think one could make some assumptions.