Laptop turns off by itself after unplugged

Go over the power management settings.
Windows has the capability to modify the power settings in both the battery-operated and plugged-in states. Your laptop can shut down after removing the power connector if the power settings have been unusually altered.

For instance, the low battery action could be altered to shut down and the low battery percentage could be fixed at 99%. When this happens, the system may power off instantly when unplugged because it thinks the battery is at a low capacity.

By checking the settings and returning them to default, you can resolve issue.

Execute the Power Troubleshooter
A built-in troubleshooting mechanism in Windows looks for the issue, finds it, and fixes it. The Power troubleshooter, one of the Windows troubleshooters, resolves laptop battery and power management problems.

An operating system's interface is provided by the BIOS of a computer, which also initialises the system's power management functions. Therefore, a flawed BIOS can affect the battery's condition and how power management functions.

Manufacturers of laptops often provide BIOS upgrades that fix flaws in the previous version. By locating the proper BIOS file, you may update the BIOS on your computer. Updates to BIOS, however, carry risks and may result in system failure.

Hope this helps. 

Hello,

Remove the charger and battery, press the power button for 60 seconds, then reconnect everything back and turn on the laptop. Let the battery charge for some time.

After some time, remove the charger. If your laptop still turns off instantly after removing the charger, your battery need to be replaced.

Good luck