I guess your letter is a closed shape like the K in image 1.
You can make a new version by applying Object > Path > Offset path with negative offset (ungroup and delete the extras) Unfortunately it's lower and narrower than the original. The grey shape below is a rectangle with the same dimensions as the bounding box of shape 1.
But nothing prevents you stretching the new version (=2) wider and higher. It's stretched to original width and height (=original bounding box dimensions) in image 3. Unfortunately I haven't found a way to make the stretching 100% automatically. Maybe a competent programmer can do it.
As well you can make a new version with positive offset and shrink it to the original width and height.
ADD: to apply the offset path to a traced bitmap image the tracing must be expanded. This generates the editable final tracing result. Before applying Object > Live trace > Expand you can still change the tracing parameters and the result isn't editable.
To get a solid black shape without a white background use tracing mode Black&White with option Ignore White=ON. It doesn't harm if the black shape is actually several separate parts.