small square progress box displayed always

Ubuntu 16.04 is end of life and no longer supported. I suggest you upgrade to 18.04 online or (recommended), wipe the install off and do a clean install of Focal (Ubuntu 20.04). This is LTS and is supported until April 2025. You can restore your user data from your backups.

Thanks for the solution !
In my case my laptop is older version so when I tried upgrading from 16.04 to higher version it leads improper installation.
Now downgraded to 16.04 where I am getting this small dot square box appeared on the screen. I doubt booting is not complete since I couldn't get into virtual console whenever I get this small square box issue. Earlier this issue was not consistent (it rectified when I reboot) but now it happen always (reboot not healing this issue now).
Any suggestion how to make booting 100%.

Does the laptop have a make and model?

My system specifications,

Dell inspiron 1525, ram 2gb, intel core 2 duo cpu T7250 @2.00ghz *2

temporary solution worked out,
sudo /etc/init.d/lightdm restart

Thanks actionparsnip, that solved my question.