When a dog adopt himself to us

So two day ago my family found this dog in our lawn at noon at first we thought nothing of it thinking it just some random neighbor dog want to have some fun with my dog(the dog in second images) but at night we saw this brown dog again and we try shoo him off but he didnt budge so my family let him stay in our lawn and with no owner,no collar and also him being pretty dirty my family just decide to keep the dog around.My guess is to why the dog stay here is either he a stray or his owner was not good with him maybe they were just being negligence and leave the door open for him get out or his owner was abusive because i saw how scare the dog was toward people and would alway bark at people