There is no way of knowing if the outside cat would kill the crippled cat until something happens, although he will continue to attack him. It depends on a great many circumstances involving both cats. Cats ages, health and fitness despite disabilites. Who has been there longest. Size and more. Although your indoor cat is crippled, is he favouring his disability or does he ignore it?
But I would suggest that if you have serious concerns, you could have the outdoor cat spayed, it may make him a little more placid, or make sure you keep the crippled cat inside at all times unless you have a cat enclosure.
It is possibly that it is simply the outdoor cat is keeping the crippled cat in line so to speak, keeping reign over his territory. The outdoor cat being the stronger of the two may just settle for giving the other a hard time when possible without harm, but this can never be guaranteed. The crippled cat needs love and attention and a certain amount of security. Personally I would try to keep the crippled cat inside as much as possible or uild a cat enclosure so he can go out if he wants t without being harrassed by the other cat.
