The phone stops fast charging and just trickle charges when the battery is full. No damage at all.
But I have heard though that if you expose the battery to trickle charges repeatedly over time that you will shorten the life span of the battery (i.e. - the amount of charging cycles until it stops being able to hold a true 100% charge anymore). Considering how fast the mobile can recharge itself (just under 2 hours for me when recharging from 10-15%), best bet would be to charge prior to bed, reboot and unplug at bedtime, and turn off all the radios you can in order to reduce discharge overnight (you'll probably only lose 3-4% by morning at worst).