OK, web site security gurus, explain to me this

[space-time]

There is a web site similar to a bank that has personal and financial information.

I was working on that web site and firefox became totally unresponsive. I had to force quit. I restarted Firefox and I was expecting to log in. But guess what? as soon as I typed in the web URL, it took me back to the same screen where it froze and I was able to continue what I did, without even logging in again, not even selecting the 3-4 clicks necessary to get there.

Is it just me or is this totally insecure? I have never seen this on any other web site. This is a web site that pretends to take security very seriously and probably handles financial information for some of you here.

[bik]

Hard to say, but it's probably OK.

The web site likely knows your IP address and knows that you were logged in on that browser (session cookie https://www.google.com/search?client=safari&rls=en&q=session+cookie&ie=UTF-8&oe=UTF-8 ).

The fact that the browser crashed is largely irrelevant. Not really any different than closing the browser window and deciding a minute later to go back and do some more business. If you didn't actually log out, it knows the browser still has an active session.

It's likely that there is a timeout for active sessions, but the browser quitting or crashing wouldn't change or accelerate that.

Edit:
Again, this is a situation where the session cookie knew it was the same computer and browser. But, before you got to that point, hopefully there was some warnings and opportunities to tell the web site whether you were using a public or private computer.

With a private computer, the site will use cookies to help remember various things to make it easier for the user. If you indicate that you're using a public or shared computer, they shouldn't "remember" stuff.