We had the same situation recently with Caramel, our nearly cat.

I had seen him around and feed him a few times and when we finally managed to catch him and get him to the vets it was bad news

He had full blown aids and tumors in his mouth that were cancerous. He was suffering and even with treatment would have continued to suffer, so we made the difficult decision to have him put to sleep *cries*

It upsets me to this day but I know we did the right thing for him.

I really feel for you to be in this difficult situation.