If your using a device and the battery goes dead thats fine. There is still juice left in it. The battery has built in circuitry to prevent it from re-charging if the voltage gets to low.
BUT the phone shuts down way before that. Its ok to let the phone shut off due to low battery as long as you charge it shortly after that happens.
What IS bad for Li-Ion and Li-Poly batteries is prolonged low voltage. So using a phone till the battery goes dead, then storing the phone or swapping batteries and forgetting to charge it.
Thats very bad for it. If the voltage gets to low the battery can not recover and will stay dead.
If its at a low critical threshold the on board circuitry will do a very slow charge to try to bring it to normal voltage and if that happens it will then allow normal / rapid charging.
Just remember when the phone shuts off due to low battery that means the battery doesnt have enough current to properly run a phone. There is still some juice left in it and its not completely dead. It still has low voltage and very little stored energy. Just make sure to re-charge it soon when its in that condition.
also keep in mind that spare batteries need to be used periodically or they can go bad. Batteries are not perfect and can self discharge very slowly over time. If your going to store a battery let it discharge in the phone till about 75% then pull it out for storage.. Then maybe once a month or two months use the battery fully for a week then put it back into storage.. OR simply rotate them. Use that for a month or two and let the other one sit..