I know a homeless family that has an injured dog, is there any kind of help for this little dog?

I think I would contact the Michigan Anti Cruelty Society in Detroit. They provide compassionate low cost or perhaps even free care for animals at their vet clinic, attached to their shelter. Most shelters will want the owner to surrender the dog

Thank you for looking out for all of them! Our nonprofit veterinary clinic at the Humane Society of Huron Valley would be happy to work with them -- phone: 734-662-4365.