Uhm, that looks like the description of a simple Web setup. But one in which scriptA does not invoke scriptB. It's more like:

1. Browser connects to server.
2. Browser makes a request to server.
3. Server calls scriptA.
4. scriptA finishes.
5. Server send output of scriptA to browser.
6. Connection terminates.
7. User goes off to buy a latte.
8. User comes back, watches some youtube videos.
9. User fills in form.
10. User hits submit.
11. Browser connects to server.
12. Browser makes request to server.
13. Server calls scriptB.
14. scriptB finishes.
15. Server sends output of scriptB to browser.
16. Connection terminates.

By default, connections used in one script will not be available in another script. But that doesn't mean you cannot use a server framework where connections are shared - but even then, a connection will only be reused if the second request comes quickly enough.