C - possible reordering issue with pipe access and mutex

Question

I have 2 threads running after write_fd was initialized by a call to pipe():

static bool finished = false;

Thread 1

pthread_mutex_lock(&lock);
if (!finished) {
    write(write_fd, buf, buf_len);
}
pthread_mutex_unlock(&lock);

Thread 2

pthread_mutex_lock(&lock);
finished = true;
pthread_mutex_unlock(&lock);
close(write_fd);

The question is whether it is possible for a compiler/cpu to reorder the instructions in Thread 2 in such a way that close(write_fd) is moved before the mutex?

If so, this might create a problem, as Thread 1 may write to a closed fd, or even worse, some other piece of code might be allocated the same fd, and Thread 1 would be writing to a wrong location.

This is a simplified form of what happens in my code. What can be done to make sure the close happens after unlocking in Thread 2, without actually moving the code into the mutex protected region? will calling the close through another function do it?