I've seen the discussions of whether NASA could imaginably have saved the crew of Columbia if they'd known about the damage to the wing in time. A lot comes down to the maximum time the crew could have survived while awaiting rescue. I haven't seen any discussion about the possibility of launching supplies to Columbia, to extend their survival time. Would that have been a possibility?
There was a faint, if-everything-went-right-and-they-decided-to-take-the-risk possibility of speeding up the launch of the next shuttle to rescue the crew. Probably not a realistic possibility.
You can read about the things that were considered in an after-the-fact analysis in the answers to this question: What would NASA have done if they knew Columbia was catastrophically damaged?
If you have an interest in the topic, I strongly urge you to read the document linked in my answer to that question. It goes through all options deemed credible in detail. If an option is not in that document, it was not deemed credible.
From that document:
There has been some discussion regarding the possibility of sending supplies to Columbia using an expendable launch vehicle – to lengthen the amount of time available to execute a rescue mission. Because of Columbiaʼs 39-degree orbital inclination, an expendable launch from a launch site with a latitude greater than 39 degrees would not be able to reach Columbia. This rules out a Soyuz/Progress launch. There was an Ariane 4 in French Guiana that successfully launched an Intelsat satellite on February 15. The challenge with developing a supply kit, building an appropriate housing and separation system, and reprogramming the Ariane seems very difficult in three weeks, although this option is still in work.
Appendix D-13 "STS-107 In-flight Options Assessment"