Homeless chicken. :-(

Hi guys, hope all you knowledgeable people can help with our issue!

We have a happy, healthy flock of 21 chickens. My mother in law lives down the street and an Araucana (not ours) showed up there out of the blue. She has asked all the neighbors and everyone around if it belongs to them, nobody has claimed it. She has chased it out of the street more than once and is worried that it is going to get killed. Of course I would be happy to add her to our flock, but I have read on here that it can be problematic and I wouldn't want the guilt of knowing our flock caused another bird harm. Our options are to try and integrate her into our flock (she is older than our birds I think, as she is laying eggs and ours haven't started), or my mother in law said she is willing to keep it. If she keeps it, should she try to get another chicken so it isn't so lonely? Would it matter if the second is a hen or rooster?

Which option do you guys think would be best? If integration is the best option, please share any/all tips you have to minimize any harm to the new lady. Our chickens have a pretty large coop/run and we let them out for a couple hours a day on the weekends (not so much anymore M-F due to daylight savings). I've read that you can add a new chicken while they are free ranging, or sleeping, or put the new chicken in a cage inside the coop, etc. but it seems like many times it is simply trial and error, and the error part worries me.

Thanks in advance for any help/advice!