If you've been seeing someone a short time and haven't made any commitments, and they buy a puppy. . .
Leave them, all the attention they should be putting into the early relationship to get it off the ground will disappear. And just forget sex/sleeping over, the puppy is like a baby that just won't give you a second alone.
If you're not living together you'll slowly be pushed out and dumped for silly reasons like "I don't have time for a relationship right now".
I've seen this happen twice in my immediate circle of friends, and once to me.