Or, they really don't know how to take proper care of themselves so how are they going to handle a dog?
Not to sound discriminating, but Section 8/welfare is the training wheels of the adult world. If you're at a stage in life where you should be responsible for, oh, I don't know, taking care of yourself, but you're at a station where need the Gov. to come in and do it for you, you really haven't shown you have what it takes to take care of a dog.
The real question is why would a landlord rent out to Section 8 in the first place? I had a friend who did that and he told me it was the worst mistake of his life.

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The Lord is my light and my salvation; whom shall I fear? The Lord is the strength of my life; of whom shall I be afraid? - Psalm 27:1