A significant number of 13-inch MacBook Pro owners from late 2013 to mid-2014 are reporting that upgrading to macOS Big Sur is killing their machines. A thread in the forums MacRumors contains quite a few users reporting the problem, and similar problems appear in Reddit and the Apple Support Communities, suggesting that the problem is widespread.
Users say that during the update to macOS Big Sur, their machines freeze showing a black screen. The key combinations for rebooting, including NVRAM, SMC, safe mode, and internet recovery, are inaccessible once the update starts, leaving the user unable to get out of the situation.
It appears that the vast majority of users who experience this dramatic situation have 13-inch MacBook Pros, from the models that came out in late 2013 and mid-2014. These are the older models that are compatible with macOS Big Sur.
It is not known what is causing the problem so, until Apple releases a patch, MacBook Pro owners from 2013 and 2014 should wait before installing macOS Big Sur.