Can a pet enjoy a good quality of life if it loses a limb?

Basil was a lovable, almost silver, mid sized, stripped tabby of no certain breed. An independent little fellow but nonetheless filled with affection in his own way. He used to fancy himself to be a hunter, but was never that successful at it, at least to the best of my knowledge he wasn't.
Only once, when Basil was not much more than a kitten, did I find an offering waiting on my kitchen floor. Now whether it was my obvious disgust about discovering half a rodent that made that the only occasion, or the fact that Basil (even when he had all four legs), was not that good at catching prey, I don't know but I suspect the latter.
More often than not Basil was out when I got home from work. He would come in when he was hungry, charging through the cat flap (pet door), and make me know, in no uncertain terms, that he was hungry. When he was home he would come running up and rub himself against my leg a couple of times, and then find himself a perch from which to observe me.
So, returning home on that late summers evening and hearing him cry out from the lounge, I knew that something was wrong.
At first, entering the room, I could hear his cries but not see him. There he was lodged tight under the stereo system. I crouched down but could not see too much of the little fellow. I reached in, scooped my arm around him and gently pulled him out. The sight of his mangled rear leg, with most of the fur missing gave me a start. Basil looked up at me with his yellow green eyes and an expression that seemed to say, "I have never asked for much from you. I made it home from the place where this happened to wait for you, all I can do is lick my wounds, but the wounds are bad, and I need your help. You will know what to do, you are my human."
I grabbed a towel and wrapped it as gently as I could around his mutilated limb. I guessed that he must have lost a lot of blood. Finding the cat carrier I settled him inside, and carried it out to my car. It was now quite late in the evening and arriving at my usual veterinarians' surgery I found it to be closed for the night. I was about to go and knock on the door and explain that I had a badly injured animal, when I remembered seeing an emergency veterinarians' office not too far away.
Moments later we were there. The lights were on, I walked in with Basil softly meowing, and explained to the receptionist that the poor chap must have been hit by a car or truck. The young lady took a look at Basil, gave him some soothing words, and called out to the veterinarian.
Not a cat that usually enjoyed being picked up by strangers, Basil the brave allowed the veterinarian to examine him without too much protest. After what seemed like an eternity the tall kindly looking "animal doctor" spoke."He's had quite an accident, it is very probable that he was thrown by the vehicle as well, but apart from the squashed leg he doesn't seem to have any other bones broken. I'm not sure what can be done, of course I will do what I can for him. Leave your details with my receptionist, go on home and I will phone you in about two hours."
I arrived home convinced that Basil the brave would have to be put to sleep. I sat thinking about him, from when he was a kitten, his futile attempts at hunting, his peculiar lovable little ways.
Eventually the phone rang. This was it, this was the veterinarian who was going to tell me that there was nothing that he could do for little Basil.
" I'm sorry..." said the veterinarian, "But I had to remove the leg."
Having been sure that he was going to tell me that Basil had been put down, on hearing that news I exclaimed " Wonderful! That's marvelous, thank you so much."
He must have thought me some kind of crazy nut, being so pleased about my pet loosing a limb!
"The amputation seems to have gone well but he will need complete rest for a while. Give my receptionist a call the day after tomorrow, and you may be able to take him home then"
The day came and I was able to bring Basil home. He had more of a stump than I imagined he would have and was able to get around with a sort of bunny hop. For the first couple of days though he did not want to do much prowling around and he kept himself indoors. On the third day when I arrived home, he was not in the flat. I went into the garden and called out for him, no sign of him at all. I went back inside feeling a little uneasy, but also pleased that he was getting back to his old self already.
Awhile later I heard the rattle of the cat flap, only it didn't sound quite the same as it usually did. On investigation I found Basil stuck half through the flap, with only 50% of his rear leg power he hadn't quite managed to get in. Not wanting to upset my surgically reduced pet by pulling him by the front legs I slowly opened the door and gently pushed him in. That was the only time, that I know of, that he got stuck, he must of quickly learned to adjust the thrust of his remaining leg.
Did his "handicap" deter him from his hunting attempts? Not a bit. He'd lay in waiting for pigeons to land in the garden, then try and rush at them, of course he never got near to a catch. Ever heard a pigeon laugh!
You know the type of garden fencing that is nothing more than thin slats of wood overlapping each other, they present a very thin top edge. Cats love to skillfully walk along them. One could be forgiven for thinking it impossible for a three legged cat, at least I did until I witnessed it. Slowly he would make his way along, his rear end seemed to drop every second step and it looked like he was about to fall. He never did, he always made it to the end.
I don't believe that Basil even knew that his leg was missing. He had a habit of sitting on his haunches, raising one hind leg and giving his ear a scratch, then repeating the process with the other leg and the other ear. He continued the habit after the accident. When it came to the missing leg, the stump would raise and waggle about and his head would turn to ensure that his ear got a good scratching from the non existent leg!
Sometimes, when folks saw Basil for the first time, they would exclaim "Poor little thing, he cant have much of a life!" Little did they know that he never let his missing leg stop him from doing the things he always had.
Basil has gone now, and I am not owned by another cat. I will save that privilege until the time I can move home to someplace with far less traffic. Whatever feline keeps me company will be wonderful I'm sure, just like Basil, who never once let his 'handicap' stop him being 100% cat.