You need to supply more information:
Which version of InDesign and OS?
What do you mean, "they weren't saved correctly"?
Are you stating you worked on a document for three days without saving it?
How do your mean, you're running out of storage?
Have you saved incremental copies of your documents?
If you close and reopen your computer are you then able to access your documents?
Never use a flash drive to read and write an active file. It may corrupt, and probably will.
Have you restarted your computer?
Never use a flash drive to read and write an active file.
I'm pretty sure you mean small-capacity flash drives like the ones we call thumb drives, but to be clear, you don't mean the SSD drives that are going into many new computers, right? Those are OK to use with active files(?)
In the US, the terms "flash drives" and "thumb drives" are pretty much used interchangeably. I think that's what Michael meant.
SSD drives are good. Flash/Thumb drives are not.