If a program runs
fork() what sets standard streams
Stdin, stdout and stderr are inherited from the parent process. It's up to the child process to change them to point to new files if that is needed.
fork(2) man page:
* The child inherits copies of the parent's set of open file descrip‐ tors. Each file descriptor in the child refers to the same open file description (see open(2)) as the corresponding file descriptor in the parent.
As Kyle Jones states, they're propagated from the parent process. If you're asking how to set them in a child, you're looking for