Glad he is back home.
My mil is romancing a cat with treats on a china dish right now. He is a lovely Tuxedo cat who lives a couple houses along. He knows a good thing. When his family is out for the day he has a warm welcome with my mil. She knows where be lives, but is happy to have the company during the day. He goes home when he hears he people's car arrive. They know where he spends his days.
In 1993 we had a starving male (intact) grey tabby show up at our house. We called the SPCA, Pound etc, but nobody had reported him missing. We had him wormed and he started to gain weight. When he was at a healthy weight we had him neutered. We called him Tom (he was a tom cat when he arrived) and referred to him as our stray cat the 14 years he lived with us. The vet figured he was 18 months to 3 years old when he moved in, so he had a good long life with us.
I tell the Tom's story so people will know that sometimes the missing cat winds up living the good life, just with another family. We tried to find his owners, but they never reported him missing, at least locally.