I'm not going to stop ya..so your asking the wrong person here.And personally..if he is a stray,shame on his owners for even giving him the opportunity to stray.I don't think they deserve to have him back.
And if he is deaf..it's a double shame shame on them.You would think they would be taking better care of him,so he does not get in harms way..
I hope you DH & you are able to give him a home he deserves.Good luck!
Sometimes, it's not the owners fault.
We had 2 Shelties. We would put them out to go potty, about 10 minutes. (Yes, alone.) One day, Misty, a 12 yo, who was mostly deaf, didn't come. My mom was in Virginia, so my dad and I took Bear, her son, out. He tracked her through our woods, and lost the scent.
We put up flyers, went house to house looking for her. We didn't find her until my mother got back, a week later. A couple had taken her, knew she was an oldie but cared for, and held her for us.
Turns out, Misty had chased a deer and gotten lost.
The dogs still go out alone at my mothers. (Not at my house, though.) They always come back, except for that one time.
But by your reckoning and judgment, we don't deserve to have them/her.