When a program exits does a database connection automatically get closed if you haven't disconnected and closed the connection in the program?

If no, would you be able to use the same connection if you still had the connection handle?

When A-Shell itself exits, every handled owned by the process should be automatically deleted.

But when a mere RUN program terminates, only the regular file channels used by the program are closed. Sockets and database connection handles should remain alive (provided you have a way of remembering the handle).