If someone i know has a baby tooth that has been in their mouth since they were little and they are 15 years old now, and the tooth is a cavity, would a permanent tooth grow in if the baby tooth is extracted?

Not Necessarily: It depends if there is a secondary tooth underneath the baby tooth. Some people are born without certain permanent teeth... it's not that uncommon. The person you know needs to see a dentist and have x-rays taken. Only with radiographs will one know if there is another tooth under the baby tooth. At a minimum that baby tooth needs to be restored, if possible.

Probably not: Over-retained baby tooth very often indicates congenitally missing permanent tooth. Sounds as if you have not seen a Dentist for a very long time. A cavity is an infection and can. cause serious complications. Please, you know what to do. See a Den test, and sooner rather than later.