The Twitter input box is much more than your average INPUT or textarea. First off, it isn't an input or textarea at all. They are instead using a well crafted DIV with a "role" attribute. for the entire text; likely capturing keystokes as they occur.
If a user is logged in, they can compose a tweet. If during that very cautious 140 character sprint, they accidentally click somewhere on the page, the browser GETs another page.
But when the user hits "back", the DIV then repopulates (after a second), with the users partially drafted tweet.
In terms of browser capability, how is this "saved form field" being accomplished?