I have a single sim with 6 dogs and I have actually had a few strays stick around. For weeks. I wasn't a member at the time so I didn't think to take pictures and I had added them to the house hold for breeding purposes over time, but I am curious if anyone knows how to cause this to happen again. I never chose to interact with the strays, my dogs did on their own sometimes, but I doubt it was a BFF related thing because I did have the dogs build relationships for breeding and to test of out the new expansion.