Disk space was scarce in that time, sustaining the usage of DoubleSpace... and write errors were common (chkdsk always found some FILE00XX.CHK lost data). When DoubleSpace was active, it was often a full partition crash instead.
I've lost so much data with DoubleSpace! Not something I miss :-)
The FILE00XX.CHK lost data may be less because of an actual error when writing, but more the result of a disk operation being interrupted. Losing power for example, or the OS crashing, resulting in "dangling" data. And in that case it's not rarely just temporary data that was meant to be free'd anyway.
OT a bit but what are you meant to do with those CHK files? Is there anything to show what they are or recover anything from them? Otherwise what's the point?
You could edit them and decide to delete them (most of the time) or rename them and get back some content (for text files at least).
Those files were created by chkdsk from orphan files (with no entry point in the directories) in the File Allocation Table (the table that gives the "FAT" name to the filesystem). After chkdsk, the filesystem was consistent again.
Such orphans appeared when the OS crashed or the system went off during file writing operations. Of course when that happened while writing on a compressed filesystem, the problem was not a lost file but a corruption. Sometimes the compressed filesystem was just entirely lost.
I've lost so much data with DoubleSpace! Not something I miss :-)