It depends a lot on the electronics of the phone and the charger. There are telephones that when the charge reaches 100% disconnect the battery charger and go to feed the phone's electronics directly from the charger whenever it is present. The battery in these cases is kept full by a minimum current.
In other cases battery power is always drained regardless of whether the charger is present or not, in these cases what Mathias Chacon says in the first response occurs. A variant of this case is that the logic of the charging circuit does not restart it until a reasonable percentage of the load has been consumed or the charger has been disconnected and reconnected. Each case involves circuits with different degrees of sophistication.
Probably in more advanced or modern phones we will find the first type of circuit while the second case and its variant can be found in older equipment or designed with a hardware platform not so advanced.
How to know in which case we are, that is a more interesting question because there is no way of knowing without eviscerating the unit and identifying the charging circuit. To complicate it, many current phones have energy saving circuits that minimize consumption when they detect that no function is being used. Such is the reduction in consumption that only the section of the telephone responsible for detecting an incoming call remains active (and at minimum power). In these phones there is almost no way to externally define what happens inside the unit by analyzing the charge current delivered by the charger. When the equipment comes to rest, consumption is practically zero.
The council, try to keep it charged whenever you can and as long as you can. Modern lithium batteries perfectly support this treatment. If the situation occurs that you reach the total exhaustion, a good recharge until it reaches the top will not hurt. There it is convenient to charge it while it is off during the night. If for some reason you have to leave it charging during the night while it is on, leave it connected to the USB port of a PC or Laptop. The charge will be slower and with less risk of damaging the battery.