If the battery is almost dead, it won't have enough power to get through the boot process, and plugging the phone in doesn't act as alternate DC power.
And if it's totally dead, it's now not a battery, it's toxic waste. (Lithium is toxic.)
Charging a totally dead lithium battery usually gets the battery so hot that it starts burning. If it doesn't, it explodes. So there's a circuit inside the battery that disconnects it from the outside world when the charge gets down to a hair above nothing.
To the original poster, if you want numbers, discharging a battery almost to 0 every day means it won't last even a year. Charging it at the 50% point every day means it should last 3-5 years. In a phone with a battery you can't change by popping the back cover off, that's kind of important. (If you need more time than 60% of the battery gives you, there are external batteries you can plug into the charging port. They come in various sizes, the largest one that I know of that's currently available is almost 10 times the capacity of the battery in your phone, so 60% of that should keep you going until you can recharge the phone and the external battery. Everyone who buys Zerolemon batteries [see Amazon] seems pleased with their performance, and with dealing with the company.)