Wait, are these homeless dogs or do they have an owner but their owner rents them out or are they technically homeless but tossed from home to home?

If it's the former, that's not such a bad idea. Kind of like fostering. But if it's the second and third idea, that's horrible, IMO. Dogs get terribly stressed and confused if they're frequently moved around from owner to owner. Unless private pet owners are using this as a daycare of sorts, I don't agree with this. Rent a pet? Pets are animals. They have feelings. They get attachment. They get lonely. To rent a dog out for whatever is convenient to you? That's ridiculous.