If there is enough data in the RAW file that you can retrieve the edges, even at the cost of the overall exposure, then you can certainly do it. I'm only familiar with Photoshop to any real depth, but I'm sure you can do something similar in the Gimp.
You will need two developments of your RAW file. One, you already have — the one where the optimum result has been achieved for most of the image. You will need a second version of the picture where the edges of the subject are distinct from the background, even if that means that most of the picture looks horribly dark. If you can keep the background pure white, that would mean bonus points, and if there's enough there to make the "lost" edges significantly different from white (say ten or more levels, with some actual colour), then you've already won the lottery. (Oh, and make them both 16-bit; that will allow you to recover without posterizing.)
Put the dark version on a level above the more correct version. Then go to the "Channels" panel and CTRL- or Command-click on the RGB channel. That will create a selection based on the luminance values in the dark image. (The marching ants will show where the 50% level is; don't worry about them.) Then go back to the layers panel and create a Curves adjustment layer. It will automatically get a luminance mask because there was a selection active when the layer was created. The mask should look like a black-and-white version of the darker image. This will make the curve you later create affect the highlights much more strongly than the midtones and shadows, and in conjunction with the curve itself will allow you to get some really fine control over the values.
Of course, that means that if you bring down the extreme highlights, you're going to lose your white background as well. You can fix that. Go back to the Channels panel and CTRL-click on the RGB to make the same luminance selection. Now, go back to the Layers panel, select the curves layer, and do a Create Group from layers. It will have its own mask, also based on the luminance values. Go to the mask and invert it (CTRL+I). You can use Levels (CTRL+L) to make most of the subject part white, leaving the background black, then use a paintbrush to finish the job/fill in the holes.
Now you have a curve available that will only affect the brightest part of the image that isn't the background. You can hide the dark version of the picture for now, and make the adjustments that bring the subject edges (and overly-light areas) back. If you find that the effect is spilling over into areas you don't want it to touch, you can put your existing group into another group (this time with no selection active) and use a soft black paintbrush on a low opacity to paint out the adjustments you don't want.
In a worst-case scenario, where colour can't be retrieved from your "good" development, you can use an intermediate version of the image with the same luminance masking and manual masking tricks to overlay good colour data on only the brightest parts of the image that aren't background, and then adjust the opacity of that overlay to get the result you want. It's a large chunk of work, but not compared to a re-shoot, and it will give you a much greater degree of control over the process than a RAW processor alone (or any global adjustments, for that matter) can give you.