From
https://en.wikipedia.org/wiki/Space_Shuttle_Columbia_disaster :
"Possible emergency procedures
In its report, the CAIB discussed potential options that could have saved Columbia's crew.[34] They determined that the mission could have originally been extended for up to 30 days, after which the lithium hydroxide canisters that were used to remove carbon dioxide would have run out.[5]: 173 On STS-107, Columbia was carrying the Extended Duration Orbiter, which increased its supply of oxygen and hydrogen.[35]: 398 To maximize the mission duration, non-essential systems would have been powered down,[35]: 399 and animals in the Spacehab module would have been euthanized.[35]: 397
"When STS-107 launched, Atlantis was undergoing preparation for the STS-114 launch on March 1, 2003. Had NASA management decided to launch a rescue mission, an expedited process could have begun to launch it as a rescue vehicle. Some pre-launch tests would have been eliminated to allow it to launch on time. Atlantis would have launched with additional equipment for EVAs, and launched with a minimum required crew. It would have rendezvoused with Columbia, and the STS-107 crew would have conducted EVAs to transfer to Atlantis. Columbia would have been remotely deorbited; as Mission Control would have been unable to remotely land it, it would have been disposed of in the Pacific Ocean.[35]: 400–404
"The CAIB also investigated the possibility of on-orbit repair of the left wing. Although there were no materials or adhesives onboard Columbia that could have survived reentry, the board researched the effectiveness of stuffing materials from the orbiter, crew cabin, or water into the RCC hole. They determined that the best option would have been to harvest tiles from other places on the orbiter, shape them, and then stuff them into the RCC hole. Given the difficulty of on-orbit repair and the risk of further damaging the RCC tiles, the CAIB determined that the likelihood of a successful on-orbit repair would have been low.[35]: 405–406"