They can and some do cut off when they’re close to full. It all depends on how sophisticated the charging system is, which roughly scales with the expense/complexity of the battery.
Running batteries way down to zero or all the way up to full is physically hard on the battery. For maximum life you want to charge up to no more than 80% or so, and not let it get down past 20% or so (depending on the battery details).
Smart charging systems know this and do it automatically (the laptop I’m typing this on holds at 80% all the time when plugged in, because I told it to). If I let it run up to 100% it would do so, then cut off the battery charging and could sit there plugged in at 100% indefinitely without battery damage.
Some car batteries have excess capacity above “100%” so they’ll say “100%” to you when they might only be at 80% of their physical capacity. That prolongs life and allows them some degradation over time without losing any range at “100%”. Some EVs with battery size options have only one physical battery, they’re just moving the 100% point in software.
At the other end of the spectrum, like cheap phones, they want to give you as much run time as they can so they run them up to 100% over and over and over, although even the most basic ones will usually have an overcharge controller that stops charging at 100% (overcharging a lithium-polymer battery, like you have in most phones, is very bad…like explode in fire bad).
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