E) Nope. There is nothing mentioned in the argument about the beliefs of people to what welfare should be.
D) The author proposes a change in the system, rather than abolotion. This is not an assumption.
C) The author does not make this claim - there is nothing in the argument about the welfare system being a safety net or not.
B) While this may be the case, it is not an assumption of the argument - there is nothing stated about welfare workers and their ability to stop/detect fraud. It could very well be the case that people are still defrauding the government, and the welfare workers know but do not stop it, or they do not know. Either way is plausible so this cannot be an assumption.
A) The correction option. Notice the phrasing of the word - "People do nothing but live off... without making an honest effort to improve..". This is the premise of the author. Suppose we had one person who was actively trying to improve? Then the author cannot say that "People do nothing but..". So this is a required assumption.
I will note that this is not a very good question - it seems to rely on wording rather than solid logic, but that is sometimes the case with third-party questions. So don't beat yourself up too much if you get this one wrong.