1.- Load an image larger than 400 x 400 pixels
2.- Acces to "Image, Size canvas" and disable "Constrain proportions"
3.- Put "400" as width and height and prees "Ok". You have now a 400x400 pixels image
4.- Activate "Crop" tool
5.- In the "Tool options", disable "Grow", enable "Will keep the width of the crop constant" and enable "Will keep the height of the crop constant".
6.- Put "400" as width value and "50" as height value (constants, in this case)
7.- Move (drag) the crop square left or right

You will see that crop square will shrink, so is not respecting the "keep the .... constant".

Hm, I guess that's because of two mutually contradictory settings: disable grow and and keep width constant. With disable grow you cannot move the crop area outside the canvas, so if you try to that, the crop area shrinks.

I'm not totally sure what would be the best thing to do here...

Well, you will choose the best option understanding what's the problem in the real work: I want to drag a crop area box whom I know the exact dimension. Just thnik the width of the area I want to crop is exactly the same than the image canvas width. so I only want to drag that delimited crop area box up and down till I view what is the best piece of the whole image that I want to get. Then, I try to drag the crop box area only up or down with my mouse pointer box, BUT I have not a precise hand movement and, despite I didn't pretend it, I move my mouse some pixels to the right and then to the left .... as result, I lost the exact width that I need!!!! The crop box will have not now a constant value, but a constant value less some pixels cause my imprecise hand movement.