They certainly do. After I put my cat down a couple of years ago (posted upthread here somewhere - kidney failure), I said pretty much the same thing you just did there, but in truth, I was in no hurry. I was kind of enjoying the freedom from taking care of him and worrying about him when I was gone.
I went 2.5 years without a cat, and was doing just fine.
But what do you do when in the dead of winter, you go outside when it’s -25F, and you see this adolescent cat wandering down the middle of the snowy street?
Well, I called him over, and he obviously wanted to come over, but he was very, very cautious. He acted half-wild, and had no collar, but didn’t appear to be starving. In fact, he seemed quite healthy, so I was sure he belonged to someone down the street. But he kept coming back and hanging around at a distance, always at night, and all of this during a cold spell of between -20F and -30F.
Finally, I went out one night and caught him huddled in front of my front door. He ran far off whe I came out, and wouldn’t come back. So, I retrieved an old can of wet cat food I had left over, and dumped in into my old cat’s dish, and went out and managed to lure him over. But he would only eat if I left the bowl and backed far away from it. And then I watched in amazement as he scarfed down an entire can of food in about 15 seconds. Night after night.
Eventually, I lured him into the house, and now, months later, he stays here all day while I’m at work, but demands to leave at night.
I do not want an indoor/outdoor cat. I want indoor only, but I’m afraid I’ve fallen in love with this guy. I suppose my next step is to get him neutered and have his shots, as I’m guessing now that nobody actually owns this cat, and so it will be up to me.
Anyway, I went off on a tangent there. Condolences, @mrcjhicks, but yes ineed, there will be another cat in your future. If you don’t go out and find one on your own, one will find you. So many cats out there need homes, and now I don’t know how I went so long without one. He is amazing, and totally worth it.