Rip first came to the ranch as a teenager, having killed his own father after the man murdered Rip’s mother and brother. Dutton brought him on and made him a ranch hand, and he was later branded by the family and swore to protect them – and the Yellowstone – no matter what. This, of course, means he’s committed multiple criminal acts, but like John Dutton, he’s in love with the land and the “cowboy” way of life that both men realize is slowly dying.
While Rip might not be his biological son, Dutton made it clear he essentially considers Rip one of his own. Neither Kayce (Luke Grimes) nor Beth would want the responsibility of running the Yellowstone following John Dutton’s death (if that’s how Costner’s character exits) while John’s estranged son Jamie is even more unlikely to take over. Rip’s love for Yellowstone is probably only matched by John, so it’s hard to picture a better successor. That said, the 1883 prophecy that the family will lose the ranch after seven generations seems to be closing in, so maybe there won’t be a successor from the clan after all.
However Costner’s Dutton ends up leaving Yellowstone, the series doesn’t have to end if Dutton gets killed. There are already reports suggesting John will die and the main series will end, but that other major characters will then continue to another spinoff series. While the popularity of offshoots like 1923 means the franchise’s future might lay outside the main show, Yellowstone is too popular to end so abruptly. If Dutton dies, seeing how the rest of the family rebuilds in the aftermath and what becomes of the ranch makes for a compelling hook in itself.