No, you can't assign a variable or anything to an unchecked check box, it merely doesn't exist in your server side script. Why don't you wana put a name for that?? You can call it by a name, like "whatever" and then check it wherever you want:
if ( !empty($_POST["whatever"]) )
// do something
But I think I know your problem! You are having your checkbox in the first page whose action is the 2nd page, when this checkbox is submitted, you can see it in the 2nd page, but when the 2nd page is itself submitted, you see nothing, right?!! Well, you have several solutions for that:
1- when the 2nd page is loaded for the first time, you can easily check if the checkbox is checked or not, then you can write it into a hidden field that you recieve it whenever the 2nd page is submitted.
2- this one is better and more systematic I think! I always use $_SERVER["PHP_SELF"] for the action of my forms. Then I check the validity of info in the same page and only if the data is valid, I transfer the user to the 2nd page. What do I do with my first page data?? Well, you can either $_SESSION them, or put them in a query string and send it to your 2nd page. Then in your 2nd page to get your data back whenever that page is submitted, you have to write an action like this:
<form action="<?=$_SERVER["PHP_SELF"] . "?" . $_SERVER["QUERY_STRING"]?>">
In case you use sessions, be careful that you empty the session when your job is finished with your forms/database, because the 2nd time that you come to the same form, you see that the data is still there!
For the 2nd solution you can make multi-paged registration forms, in which you don't get all the info in only one page.