My MacBook Air running on Big sur had 12 GB of empty space and suddenly jumped down to 1 GB.

What is “Other” storage on a Mac, and how can I clean it out?

See used and available storage space on your Mac

From Apple Document from above link

• Other: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

You are living in dangerous territory if your drive had only 12GB free to begin with.

The OS will use part of the space of your drive for caches, virtual memory and stuff. As so, the free space will fluctuate.

Furthermore, any drive, and especially the system drive, should always have some 10-15% (some say 20%) free at all times.

Attention: If this condition is not addressed / fixed Right Away - the computer could and will eventually Stop working at all - period. Then whatever is on the drive is in great jeopardy of being lost.

And, the amount occupied will change all the time. Some of it could be snapshots from local Time Machine backups which should disappear once you plug in Time Machine and update backups.

You need to maintain an absolute minimum of 15 - 20 GB of empty space at all times because your "storage" space also contains a working operating system which needs space to function or it will simply stop as mentioned.

So, get an external drive now and offload some space hogging stuff like pics, movies, videos, etc.