Should I take their dog?

My cousin has a dog.. and she doesn’t take good care of it. It’s some sort of French bulldog or something. But she just keeps it in the backyard. Morning, noon, night.. right now it’s raining, and cold outside, and the dogs outside. Yes the dog does have shelter. But it’s a tiny dog, I know she’s cold. Every time I come over I make sure she has food and water, because she just an after thought to my cousin. I feel bad.. I don’t want the dog, I have two German shepherds at home, who are inside dogs.. so that won’t work. But I feel like I could find her a good home.. last time the dog got out and they kept her at the pound or wherever she was for over a month cause of my cousins laziness. Ido what to do.. I know it’s not my dog, but they only live so long, I want her to be happy and loved.. and I feel like she’s depressed and miserable.. she gets sick often cause they just leave her out in the cold, ear infections that they don’t bother to take care of diligently, etc.. 😢