Hello, I want to ask is it possible for a person who got depression recovers by herself? And she's an introvert person.

of course it is possible.
in fact a lot of person do have a significant episode of mental illness during their lifetime.
a lot of them recover well.

but, good to keep an eye without being intrusive.

No one could tell what's the possibility, depending on how she deals with problems. If she's an introvert, there is a likelihood that she will suppress her emotions instead and that is akin to a time bomb. Apart from bringing adverse effect, she will one day explode or reach a lowest point.

I suggest she speak to someone in the family/ among her friends whom she can believe in, or someone who can give good advice/ guidance. If this person detects that it's severe, seek professional help. There's nothing like getting a 3rd party intervention to help see things from a new perspective.