I've seen in some major cities (ie NYC, Chicago, DC, LA) where homeless people did in fact have pets. They do have access to basic care through programs through the city. I think this is a great program actually so I don't think this limits people who may want a dog.
Further to this, people who have low incomes, lets say below the poverty line which is ~36K/year, I've seen families give loving, happy, healthy homes to a pet.
Just because someone doesn't make a substantial amount of money does not make them unqualified to own a pet. Time and responsibility makes owning a pet possible. Granted there are costs that may come up that make be rate limiting (example dog gets cancer or breaks something) the pet parent may make the hard choice to put that dog down instead of give chemo or 5k surgery. It doesn't take away from their love for the pet or the life they may have provided for that animal. We can't judge anyone for that because they may be taking funds and resources from a child or an elderly parent they are taking care of. Everyone's life has circumstances and an individual has their own right to know which circumstances will allow them to make a responsible choice in owning a pet or not.
So my two cents is that yes a low income person can own a pet.
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