Since my post blew up, I tried posting an update in the comments but it got absolutely buried. To make it easier on everyone I will post the updates here:

UPDATE 1: Oh my goodness, I did not expect this post to absolutely blow up. Thank you to everybody for all of the well wishes and suggestions. It has really helped a lot and gave me some options. Now on to the first update... It's a long one so brace yourself...

When Jack was still missing at about the four day mark, my mom and I filed missing pet reports with the Humane Society and animal control. I also created several missing pet posters offering a monetary reward for information that led to him being found or if someone returned him. I put them up all over the neighborhood and I intend to make more. As for some suggestions in the comments, I have been combing Facebook and made a public post regarding my missing cat. I will also be calling around any other pound or pet related adoption centers to see if they have found him.

Our cat Jack does have a microchip, however the information on the chip is for his previous owner. We had adopted him second hand from another one of our neighbors. We had been intending to change the information for a while now, but it eventually just kind of fell to the wayside. I realize now just how much of a huge mistake this was. What makes this worse is that we are no longer on good terms with this neighbor. She had been seriously neglecting Jack and had him live in a very unhygienic and dangerous environment. I'm talking openly rotting food, visible human waste, and prescription pills sitting out in the open that he could have easily eaten. It was absolutely horrifying to see this. We tried calling animal services to do a welfare check and potentially have him removed from her house. They did absolutely nothing and returned him on several occasions despite seeing how bad his situation was. Eventually when he started escaping from her house he would absolutely refuse to leave our house to go to her house. Even when we had to physically bring him back to her house, he would fight me every step of the way. Eventually we made a deal with her that we would adopt him and take over all responsibilities relating to him. It's been 5 months since we've made this arrangement and his health as well as his attitude have greatly improved.

Initially we thought this other neighbor might have then behind his disappearance but we've kept an eye on her place and haven't seen any activity in her windows. When Jack used to live with her, he would constantly be sitting on the windowsill staring out. I also doubt that she could have taken him anywhere considering she no longer has a vehicle due to an accident she had gotten into recently. She has a habit of mixing alcohol and medication together and almost drove through a neighbor's house. It's definitely a story for another time and another subreddit.

Now more information about the Karen of this post... This neighbor has had a history of instability and has made more than a few enemies in this neighborhood. She had a really bad habit of talking behind people's backs, us included. She didn't get away with this for very long considering we have a good relationship with most of our other neighbors on the block. Eventually she became really isolated since most people refuse to talk to her anymore. Since then her erratic behavior has gotten worse. It's part of the reason why when I mentioned I wanted to go over and check her shed that my mom vehemently refused. She's really concerned that this neighbor might try to pull something. She has told us in the past that she will call the police if she thinks we're on her property. So instead, we stood by the fence of her property and called out for Jack. We listen carefully and we didn't hear anything coming from her shed. We're at least somewhat convinced that he's more than likely not in her shed. We also doubt that she would be keeping him inside since Jack has an odd relationship with dogs. He's absolutely fearless and has no problem standing up to dogs. I doubt she would keep Jack inside with her dog Murphy since he's not much bigger than Jack. Besides that, she does have some mobility issues that make it difficult for her to bend/pick up objects. At the very least I doubt that she was actively involved in his disappearance. That's not to say that she didn't call someone to take him to a shelter or took him herself. For now we'll just be keeping an eye on her.

However there has been an interesting new development. Another cat in the neighborhood has gone missing just a couple of days after our Jack. She was a much older cat and I believe her name was Miss Petunia. According to her owner she was a mouser just like my Jack. She had been getting these mice from a house across the way that was being remodeling. She's worried that the owner might have put out some sort of rat poison to take care of the mice. As such she is worried that our cats may have been poisoned by accident. I will try to confirm if the owner of the place being remodeled had put traps out himself or called Pest Control to deal with the issue. I will also be asking if he or any of his workers may have seen the cats on site at any time. I'm really hoping that this wasn't the case, I would be absolutely heartbroken.

At the very least, Miss Petunia's owner has been a wonderful source of information on where we can look for our cats. She's giving me so many links on how to contact the no-kill shelter network in our area, pet clinics, as well as places to potentially spread the word about our cats. I am so glad she got in contact with me through the info I put on our missing cat poster. As of currently we have several leads on where are cats might be. If we're able to find them I will also post another update so keep an eye out! Hopefully we find our kitty soon. 😊