Is there a way to distribute editable global variable string across multiprocessing and threads?

You gave few details about your code; the OP doesn't offer a repex.

Across threads is straightforward. Though you probably want to protect access with a mutex.

Across processes implies writing to a file descriptor, such as a pipe or an mmap'd file. Easiest thing to do would be to append lines to a log file, or INSERT rows in a relational database.