A thought struck me while reading these questions.

Suppose there was a magical child in a pureblood family, who shows signs of being magical early and gets their Hogwarts letter on their eleventh birthday. They arrive at Hogwarts and start their education, but shortly afterwards, lose their ability to do magic. Not that they are a bad witch or wizard but they are completely incapable of doing magic. Is it possible?

Conversely, is it possible for a muggle to gain wizarding powers through teenage years, having no magical family?