The answer to the original question is: No.
Let’s consider the process of charging a cell with a benchtop power supply, which can be especially useful for charging small cells like rechargeable coin cells.
The process of charging a cell with a benchtop power supply is:
Set the voltage limit to the desired charge termination voltage, such as 4.2V.
Set the current limit to the maximum current you wish to charge at, such as 1/3C, which would be 1000mA for a 3000mAh cell.
Terminate the charge in accordance with the cell’s datasheet.
The power supply will provide constant current and constant voltage, CCCV, automatically as the cell charges.
It may at first provide a constant current (CC) at the current limit you’ve set, and the voltage will be variable, eventually climbing up to the set voltage limit.
Once the set voltage limit is reached, the voltage will be constant (CV) and the current draw will slowly drop as the voltage of the cell gets closer to the supply voltage.
A proper charge cycle of a liion cell is supposed to be terminated not when the current drops to zero, but when it reaches a certain low value, such as C/20, which for a 3000mAh cell is: 3000 / 20 = 150mA. Refer to the liion cell’s datasheet for this specification.
The Samsung 50S datasheet for example says: “Standard charge CCCV, 2.5A, 4.20 V, 250mA cut-off.” The 50S is a 5000mAh cell, so 2.5A is a C/2 charge rate, and 250mA cut-off is C/20. If you don’t have a datasheet, but know the capacity of the cell you’re charging, you could use a typical current value such as C/2 or C/3, and a typical termination current such as C/20. If you leave the cell charging beyond this point and the current draw goes even lower, it’s not a problem.
At least one cell specifies a cutoff current of .01C in the datasheet (Pytes/DLG INR18650-320) which for that cell is a cutoff of just 35mA.
Eventually the current will drop to nearly zero but this takes a long time.
Some sources [1, 2] claim that leaving a lithium ion cell charging can damage the cell. This has been discussed on some forums here and here. After looking into this, I believe that while long duration “float charging” at 4.2V is in fact bad for the life of the cell, it is of little concern within the short time frames of typical charging sessions. Here’s an article that talks about long duration float charging of liion cells: “In float charging, current entry beyond full charge is prevented by choosing a charge voltage less than or equal to the voltage naturally produced by the cell at full charge – which depends on the cell’s exact electrochemistry and temperature.”
In certain industrial applications, liion cells are actually float charged. This should be done at a voltage less than or equal to the “resting voltage” of the cell after a normal charge cycle per datasheet specifications. In other words, if you performed a charge to 4.2V and the cutoff as per the datasheet and then let the cell rest for a day or whatever, and after which you found the voltage resting at 4.18V, this would be the voltage you would not want to “float charge” beyond. I’m not advocating float charging, just making the point that if you were performing a liion charge cycle with a power supply and did not want to monitor the termination current at all, setting the voltage to a low enough value, for example 4.15V or lower, would be a sensible approach.
Typical smart chargers for lithium cells will automatically stop the charge cycle at a certain current, like 100mA or something like that. Look at HKJ’s charger tests for examples of this. Some chargers will restart the charge cycle if the voltage of the cell drops below a certain value, such as 4.0V, if you were to leave the cell in the charger. Some chargers exhibit a small parasitic drain on the cell which would drain the cell over an extended period of time. It is not advisable to leave a cell in a charger indefinitely.
What could make a liion cell self destruct is charging beyond the specified maximum charge voltage in the cell’s datasheet. A typical liion cell with have a charge termination voltage specified as: 4.20 ± 0.05 V, meaning the maximum allowable charge voltage would be 4.25V.
4.2V ± 0.05 V allows for some inaccuracy. Chargers should not be providing a voltage above 4.25V as an absolute maximum.
Also problematic is reviving a dead cell, such as one with a voltage below 2.0V. Refer to HKJ’s article about this.