How can welfare be a parnassah?
When welfare provides you with many of the things you would normally be spending income on, that is called living on welfare. Not sure how else it can be used or understood.
People collecting welfare benefits do not do anything or contribute anything for them. If they have a low paying job, that is compensation for goods and services.
“They do not give you these services if they don’t think that you are doing something that is contributing to society. You have to prove that you are working or studying a certain amount of hours a week (at least for some of these services if not all)”
That is not true for welfare. Your requirement is to have little assets and low reported income. Your unwritten requirement is to be honest about your income.