What happens to info entered into https session if the session errors out

Hi,

I simply need to confirm, as confidently as possible, that data entered into a form in an HTTPS browser session is secure, even if that web site generates an error mid-session and leaves one with no choice but to close the browser.

I know one must go into browser settings/history and delete history/cookies/etc.  But ... can I be really really sure that the data entered into that form didn't "go somewhere."

It may seem like a silly Q ... but I have active, current, and real concerns about possible ID theft that I need to research ASAP ... and I just entered non-public data into a trusted web site, only to have the bleeping web site fail on me halfway through.