A month or so before my daughter's first birthday, we put her in her stroller and took her for a walk down by the river, not far from where we lived at the time. A few blocks into our walk we met a cat and stopped to say hello to it. It was a young cat, very friendly, and when we walked away it started following us. Every now and then it would head up the front walk of a house we were passing, but then it would turn around and hurry to catch up with us.
There was a small embankment between us and the houses along that street, so every one of them had a few steps in its front walk. The embankment didn't run straight - it meandered a bit, so at some houses those steps were right out at the end of the walk, where it joined the sidewalk along the street, while at others they were set back, closer to the house. And it didn't take us long to notice that whenever the cat stopped to investigate a house, it was always one where those steps in the front walk were right out next to the sidewalk. So we figured the cat was lost, and while it didn't know where Home was, it knew what Home ought to look like.
It had been following us for several blocks when a woman out working in her garden as we passed commented on what a pretty cat we had. We explained that it was a stray that had attached itself to us, and she offfered to loan us a cat carrier so the poor cat wouldn't have to walk all the way to our house, which was still a few blocks away. We accepted and carried it the rest of the way home.
The next morning we printed up some "FOUND CAT" signs and set out to post them in the area where we'd found the cat. Just after we finished attaching the first sign to a telephone pole two teen-aged girls came up and stopped to see what we were doing. After reading our poster one of the girls said, "Oh, that's Megan's cat!" My wife recognised Megan's name - she was a young lady who had been murdered a week or so earlier by her estranged husband - and remembered her address, so we walked over to have a look at her house. It was a block or two from where we'd first met the cat, and sure enough, it had steps at the end of its front walk, right out at the sidewalk.
So we went back home and discussed the cat. She was a grey tabby, similar to one we'd lost the year before, very friendly, and she seemed to get on well with our other two cats, so we decided to keep her. According to the vet we took her to she was around a year old, or perhaps a bit more - a month or few older than our daughter. We picked the name Seshet* from a list of Egyptian goddesses, and she settled right in.
A year later we transferred from Norfolk to Groton. We were only allowed two cats in Navy housing, and we still had two of the three my wife had had before we were married, so Seshet went to live with my in-laws, in the next town over. The other two cats died over the course of the next few years, but by then Seshet had become used to being an indoor/outdoor cat, which wasn't permitted in housing, so she stayed on at my in-laws' place, even after I retired and we moved out of housing. She's still officially our cat, though, not theirs.
It's now a few weeks shy of eighteen years since that walk with our daughter and a poor, lost cat. Seshet has gone deaf, and arthritis has set in; she can still jump up onto the porch railing, but she can't sit properly - she squats, with her butt still an inch or so off the ground - and she's no longer flexible enough to clean herself properly. Recently she's begun losing bladder control, and forgets to use the litter box. So it's been decided that tomorrow she'll make her final visit to the vet....
We'll miss her.
* Wikipedia prefers the spelling "Seshat."