IMO bioprof, you came close to what is happening with the lye water.
Actually, it isn't exactly the "softer parts" of the wood, it's the endgrain of the wood.
If you folks would take a close look at this little drawing I made you can see that the grain in curly maple (or any other 'curly' wood) actually does curl. It is shaped into waves.
When the wave is running parallel to the surface of the wood it acts like plain old wood when stains or solutions like aquafortis is applied. Some of it soaks in but not a lot.
When the wave is coming up (or going down) it exposes the ends of the grain very similar to the grain on the end of a piece of board. We all know how unprotected end grain soaks up fluids.
Anyway, at the risk of raising a few hackles here I will say that putting a good built up finish on the wood is as important if not more important than the stains a person uses if they are really interested in showing off the curl of the finished stock.
I've finished a few guns with satin finishes and they just don't show up the translucent "look" that curly woods are capable of developing.
Just a few coats of linseed oil for instance will darken the overall color of the wood and the stripes will be visible but the stripes will not "stand out".
Building up a thicker layer of finish and leaving it a bit more shiny allows the light to penetrate and brings out the stripes better.
Giving the built up finish a polished look really shows off the wood the best.
Think of it as you would a creek.
If there is no water in it the still wet bottom will look like... a wet bottom.
If there is water in the creek but a breeze roughens the surface, the bottom can be seen but it is hard to make out the individual features.
If the creek isn't flowing so the surface is glass smooth, you can see every little feature on the bottom.
Of course this is based on the water being totally clear. If the water is somewhat muddy you will never see the bottom clearly and this is exactly what a person will get if they use a pre-colored oil based stain.