Unlike other MCU heroes who have gotten their powers from one of the Infinity Stones, Captain Marvel got hers directly from the Tesseract (also known as the Space Stone). She is imbued with the power of this special artifact, and it’s pretty likely that she will have the ability to destroy an Infinity Stone in Endgame.
The first Infinity Stone appeared in Captain America: The First Avenger, where Red Skull used the item to power his evil war machines. It was later stolen by Howard Stark and eventually given to Tony Stark to keep it safe.
This is the same Infinity Stone that Hydra manipulated to give Wanda and Pietro Maximoff superhuman abilities in Avengers: Age of Ultron. Using the Mind Stone, Hydra made the fraternal twins completely different people – Wanda was granted telekinesis and some mind control, while Pietro got super-speed.
It’s not as if this process was all that unhinged, and it seems to be much more controlled in the MCU than what Carol experienced. In fact, in the TV show WandaVision, the HYDRA agent Baron Strucker even goes so far as to experiment on his subjects in a controlled lab environment.
It’s likely that Marvel will be able to use her own powers to destroy an Infinity Stone in Endgame, and there are some very valid reasons why it should be possible. First, the Tesseract has been around for decades in both Earth and Asgard. It’s also the source of Carol Danvers’ powers, so she should be able to shatter the Space Stone just like Wanda did with the Mind Stone.