I wouldn't plug a phone in to charge that still shows 100% or 99% but 90% or 95% is fine. Unless they've changed the way phones charge since I first learnt about them, they charge in two different stages. Fast when the battery is low (20%) then slows down at the upper levels (80 to 90%.) That's why a phone can charge from 20% to 30% in 10 minutes, let's say for example, and also do 30% to 40% also in ten minutes. But when it gets to 95% it can take ten minutes just to get to 97%, which is a movement of 2% compared compared to 10% before, because it's charging fast then, and slows down as it becomes fuller. The charger actually gets its dictates from the batteries voltage. That percent gauge is just for your convenience. So when you plug in a lithium device to charge, several things happen at once. One of those things is determining which stage to charge in. If the battery is below a certain threshold voltage, it starts charging fast, like when the battery is at 40%. If it detects the voltage is above that threshold, it then commands it to charge at that slower pace. I remember experimenting with this in an old ZTE phone, my first ever smartphone. When charging from 25% the charger would be warm. But if I plugged it in at 92% the charger would produce very very very little to no heat in the charger block as the phone went to 100%.
That's how lithium batteries have worked from since I've started fooling with them, and if they've changed, it's news to me. Your battery has several protections built in, from overcharge to over discharge protection. Over current protection as well, but you really only see this happening in cordless tools that you try to draw to much power from. They also have a protection built in that if they get too overdischarged from self discharge and the voltage drops below a safe level, the circuit opens and renders the battery from accepting any charge unless you've got like a cadex battery analyzer.
Probably a longer answer than you wanted, but there it is.