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First off, you need to let us know what version of Illustrator you're working in because if this "Box" is the page size or art board it will be working and is controlled in different ways in each version. If you are trying to resolve an issue it always helps to post an screen shot image of what you're working on so as to better illustrate the "Box" you're referring to. Only saves what is in the "small box"? Now you refer to another box as a small box, with such vague disscriptions it could ba any number of things: a mask, the bounds of the art board, the page size… If you go View>Show/Hide Art board does this "Box" seem to disappear? Does this "Box" highlight when you click on? If so, can you direct select it with the option key held down and delete it, thus exposing more of the image? Answers to these questions will help me figure out what your are referring to as "This Box" and "Small Box".
You can attach files with the paper clip at the bottom of the forum page and Insert images or screen shots with the camera icon.
If the "box" is a black box that you cannot select, it is likely the boundaries of your artboard. If you're trying to open a raster image (jpg, tiff, gif, png, bmp) with Illustrator, it will open that image as a linked file on whatever your default artboard is. You can modify your artboard by going to File>Document Setup and resizing it to match your image dimesions.
OH THANKS! Sorry I was so vague with my description. I am using illustrator cs4.
You were right it was the artboard and it disappeard. Thanks!
Using View>Hide Artboard doesn't make the box "go away," rather it simply makes it invisible. If you are having trouble with the file only saving the portion of the image within the artboard, hiding the artboard isn't going to help you with that (if you resized it, then it shouldn't matter.)
Out of curiosity, what method were you using to save your file that is causing the image to be cropped by the artboard? That shouldn't happen if you are saving it as an .ai file. The only way that should be happening is if you are exporting (ex. PDF, or Save to Web with "clip to artboard" selected). When you try to save the file now, is it saving all of the image?