Hello & welcome to Just Answer/Pearl. I am Dr. B, a licensed veterinarian and I would like to help you with your wee one today.
I am so sorry to hear that your lad is doing so poorly. First, I would note that rabies is very unlikely. Both because the exposure was too long ago (often true rabies infection leads to the animal dying about two weeks after they contract the virus) and his signs are more likely indicating other issues of old age for him.
First, we have to consider his appetite decline, the licking, terrible smell, wet chin and drooling. These are all signs that are very common of a cat with dental disease or can be related to kidney struggles. For dental disease, we often see older cats suffer from tooth decay which leads to mouth pain. And if a cat has a sore mouth, they may drool, lick (as if to displace the irritant), paw at their mouth, suffer from appetite depression and even anorexia (which then leads on to weakness and lethargy). As well, the teeth and gums will often become infected by bacteria giving rise to oral odor but also odor in the saliva (which he then covers his coat with when he bathes). So, this would be a high suspicion for your wee one.
The other consideration is kidney disease. While you may not be aware, kidney failure kitties can develop uremic (ammonia scented) breath when their condition is severe. Furthermore, we will see secondary ulcerations of the mouth or throat with kidney disease which may again cause oral pain and its associated chain of events. So, this too could be related to what you have been seeing with him.
Now more worryingly is his collapse and current state. Initially your history made me suspicious of severe arthritis causing his weakness and the wobbliness you have seen. But the issue with this weak back leg and his vocalizing/respiratory signs does may me worry that he may have a more sinister problem at this stage. As well, you have noted that he can only move one of the back legs. If he is truly unable to move the other back leg (or if it feels cooler then the other or if you pinch a toe on that foot and he cannot feel it) then we have to consider that he may have thrown a clot which is now blocking blood flow to that back leg. And if this is the case, then he will be vocalizing due to severe pain and his prognosis of getting through this will be even poorer then it already is.
In this situation, I am sure you understand that he should not be left to linger. I am afraid that given all that you have described that he is suffering now and that it is his time. Rabies is quite unlikely here (so your husband doesn't have to worry about that) but I am concerned that your kitty may have a clot lodged in one of his blood vessels and this is now causing paralysis of that back leg and significant pain. Therefore, we do really need to consider having him evaluated and likely put to sleep at this stage.
Now I completely appreciate that you do not want to take him to the vet's office. But as I am sure you understand, there will not be really be a humane way to put him down at home without the aid of a vet (since the drugs that are used are very tightly controlled since they could be used to harm people if they were being used improperly). Therefore, I would strongly advise phoning you vet and requesting a house visit (some will). Otherwise, you may want to consider using a mobile vet in your area. These are vets that will come to you rather then maintain their own practice. You can find one local to you via the Housecall Vet Database (LINK) or your own vet may know of those local to yourselves.
Overall, his signs do point to some serious end stage issues and I am concerned that his most recent signs are a turn for the worse. Therefore, I would strongly advise seeing if his vet can come to him and aid him in his time of need. That way he can go peacefully at home and not have to struggle anymore.
I hope this information is helpful.
Please do let me know if you have any further questions.
If you have no further questions, feedback is greatly appreciated.
All the best,
Please remember to only rate my answer when you are satisfied. IF you have any lingering questions or concerns, please stop and reply to me via the REPLY or CONTINUE CONVERSATION button with the issue you have. I will be happy to continue further and do everything I can to provide you with the service you seek. If you are satisfied, please click the 4-5 stars or associated happy face so that I may receive credit for my assistance.