If your indoor cat is ailing, it needs vet care. Doesn’t mean the cat should be outdoors. Could be a sign of age, an illness, maybe improper diet. An unhealthy coat could be a sign of illness, but it could also mean the cat needs more frequent brushing.
Statistically, indoor cats live longer than outdoor cats. An outdoor cat lives on average five years. The average lifespan for an indoor cat is 15. A close friend’s indoor cat lived to age 21. Give a cat the proper diet, plenty of exercise and regular vet care, and it can live a long time.
As a volunteer with the ASPCA, I know ferals (not wandering house cats) live to around 5 years but those in trap/neuter/release programs live up to 12 years. My new indoor/outdoor cat (she belonged to my aging mother) is close to around 12. She’s got the most beautiful coat I’ve ever seen. She’s had quite a nice life - filled with adventure.
Indoor cats don’t live longer - it just feels like it!