Agree. With my Rezound after some discharges and recharges, the phone seems to pick up a user pattern based on your settings. At the end of my first week of use, I could easily get 1-2 days of light/medium use with the standard battery. Your mileage may vary.
I hear people say this often, but I'm pretty sure that it is not the case of your phone "learning the usage pattern." Lithium-ion batteries have a break in period and need a few charges before they can achieve their full capacity. I think this battery characteristic makes people think it's the phone that is acting differently, when really it is the battery that is acting differently.
Anyway, to answer the question, A lithium-ion battery should never be technically "fully discharged". The phone should shut off at a certain voltage to prevent this. However, I've read a number of posts from people saying their phone no longer charges a battery that they've run down completely. This makes me wonder if the phone isn't properly reacting to the cutoff voltage. So, if you can help it, I wouldn't let the phone run down until it shuts itself off.
Personally, I recharge at around 40% in order to have more recharge cycles.
Here's a good, albeit technical, reference:
Charging Litum-Ion Batteries