https://www.edmunds.com/nissan/leaf/2011/long-term-road-test/2011-nissan-leaf-driving-it-to-the-bitter-end.html has a video of a Leaf driven until dead. The % state of charge display didn't arrive until model year '13.
If you really like driving around near the bottom, you should get Leaf Spy (and OBD2 dongle compatible w/Leaf Spy the version for your phone OS). The % SoC display can go from around 5 or 6% to ---%. I've been there. :/ You may not see 5, 4, 3, 2, 1%.
IIRC, there's LBW (low battery warning), Very LBW (VLBW), turtle then dead. I think the GOM becomes --- miles at VLBW.