As for me, "Safe mode" has been the remedy for this problem. As soon as MacBook starts running, switch on "safe mode" for software operation (by holding down the left "SHIFT" key until you can see on your computer screen a login box to enter a password. Afterwards, run the update Big Sur 11.1.11. installation. It has worked in my case and the issue is fixed now.

I have experienced the same thing three times in a row so far. I have been trying to download the MacOS Big Sur 11.11.1. update but the process cannot be terminated on my Apple Computer (13 inch MacBook Pro, 2019). Everything has simply come to a halt and the notice: "10 minutes remaining" is still displayed. I have been waiting for three hours and nothing happens at the moment. However, Mac is just loud while working. I would be grateful for any hint or tip on how this troublesome issue could be fixed or resolved. Perhaps it could be better to skip this hard luck update or to wait for another one when the bug is already fixed.