An interesting effect I've found, you can reproduce it with Photoshop CS4 as well. Set the working space as sRGB, intent relative colorimetric, no BPC. Then using color picker enter this Lab value:
0, -120, 0
As you can see, the obtained RGB values are 0, 0, 0. So far so good. Or not? Try this other Lab value:
0, 0, -120
Oops! now we got 0, 27, 182! What's happening? The answer, as far as I can tell, is clipping. If you take the work (I did) of implementing Lab -> XYZ and then XYZ -> sRGB by using entirely floating point formulas, the second value of 0, 0, -120 getting converted to some color with lots of L* is just a consequence of the math. From where it comes all this L*?
lcms does clip negative XYZ numbers, so in both you will obtain 0, 0, 0. What makes me wonder is why photoshop does clip one axis (a) and does not clip the other (b) in the same fashion?
Maybe is just clipping XYZ negative numbers? Ok. lcms2 gives 0, 48, 0 for a Lab of 0, 0, -120. This is the result of not clipping anything at middle stages and letting XYZ negative numbers as well. Clipping happens only on the last stage or when is absolutely required (indexing LUTs, for example). I guess more experimentation is needed in this part...