Discussion, talk and tips
https://forum.puppylinux.com/
In Windows, you eject the USB stick before physically removing it. That prevents damage to the filesystem on the stick. You can also set the USB ports to be hot swapable.
What to do in Puppy?
Right click the USB icon in the lower left of the display, choose Unmount. Wait for the mounted indicator to disappear. Remove.
wizard
Here's another way. 
A USB thumbdrive is 'practically' a disk.
A disk can have multiple partitions.
You have to unmount ALL disk partitions for a particular disk to safely remove it.
Thumbdrives usually have 1 partition.
If so, remove it by:
Right-clicking the USB desktop icon and selecting the unmount partition option (flash will have an obvious different icon than a disk partition)
Right-clicking the mount folder in ROX-Filer (and selecting "Unmount")
Entering umount /mnt/[your partition] in a terminal prompt
Times the system does not want you to unmount, in which case it usually provides feedback (e.g., cli/option 3).
Something as simple as having a terminal window open with your flash partition as the working directory will prevent you from unmounting it, having a loaded .sfs on it, the pupsave, etc.
Things to consider.
Just left-click on the mount indicator in the upper right corner of the drive icon and wait until it dissapears...
To safely remove a USB drive.
Make sure it is unmounted before removing.
Simple way is use the drive icon displayed on the lower left of the desktop.
There will be a icon for each partition of each drive in the computer.
So the USB drive may have several icons on the desktop.
Example:
USB drive is identified as sdc.
It has two partitions.
The desktop drive icons for the USB drive will be sdc1 and sdc2.
So make sure both icons are not showing the mount indicator (top right of icon)
If the save file/folder is on the drive partition.
You can not unmount it.
That partition needs to stay mounted.
bigpup "...
Thumbdrives usually have 1 partition.
... Entering umount /mnt/[your partition] in a terminal prompt
Times the system does not want you to unmount, in which case it usually provides feedback (e.g., cli/option 3)."
Just following up the above. When you Right-Click the Launcher you'll see one of your choices is "Unmount ALL mounted partitions". It initiates what it says.
If you've recently written to or from the USB-Key, especially if it involves large file(s) and your Key does not light-up and blink periodically to show activity, that activity may still be taking place. For example, say you are copying a 1.5 Gb ISO to or from the USB-Key. A window to the location being written to may immediately show the ISO file, but completion of writing may take several minutes, especially if your System is engaged in other moving/copying activities.
To insure that writing to or from the Key is completed, open a terminal and type, code:
sync
The terminal's prompt will not return while copying/moving of files is in progress.
This, again, is one area of "why" I raised a concern in the "BUG Report" portion of this forum.
If you remove a USB without unmounting the drive(s) in almost ALL cases, no physical harm or data corruption will occur on the USB/SDcards.
The ONLY time ANY data corruption can occur is when the system is continuing to "write" to the drive (called 'lazy-write' in some development circles because completion I/O buffer(s) is being emptied to the drive) when the USB is ejected/pulled/powered off. So, in most cases, this is not a problem AND for some USB that have a light, if it is flashing a read-write operation is currently active on the unit.
In any case, I AGREE that a safe practice is to 'umount' all partitions on the drive. But, humans make mistakes constantly and in PUPs, we have phantom mount-points active in the running system even as no device to it is present. Thus, phantom mount-points is a bug; albeit a low-priority bug...still a bug.
FYI
Slightly off-topic but related.
Reading this thread I note that if the drive icons on the desktop had a little flashing light to let you know it was being used could be handy.
Sometimes I watch Xload, it looks like a TV set too.
That's a nominal idea, and it would apply to ALL I/O devices where the 'lazy-write' operations are active during system's operations. It would give a visual understanding of one's system's behavior and could improve human behavior.
BUT does not address "normal" the human behavior factor of these removable I/O devices. Good practice and human behavior even for the seasoned ones of us, is a quick action that in 99% of cases would not affect unit's data because for most us the unit was sitting idle before we removed it or...
But removal without umounts leaves artifacts aka "phantom" mount-points. These are a bug.
P.S. I have noticed that MS, though gives good advice when USB are plugged in, does not 'seem' to leave phantom artifacts scattered across the OS's file system. And, MS alert users on BOTH plug-in as well as removals of these removable unit. But, as is the case with us, here, the removal in MS without unmounting remains the same.
Thanks @dogcat
Before making my post, I had tried right-clicking the drive's icon and selecting to unmount. Being color blind, I did not notice the tiny square badge in the icon changing. I do notice it now, only because I know to look for the subtle difference. [Most things in Fossa are that way re: color blindness. And besides color, there is also a *lot* of low-contrast that's used all over. I did change the icon set to one that's better.] I'm not asking for things to be changed, just noting that they exist that way.
I had also found the pMount utility, but noticed that clicking unmount on the C: (Windows) drive did nothing. I now know that it can't be unmounted when in use. That's when I posted my question.
I did like the USB sticks with a light, but haven't seen one in years. With M$oft, the light would come on at random times, so something was scanning for no apparent reason. Thereafter, I would usually eject sticks when not in use, without removing them. [Similarly, after I stopped using spyware Chrome years ago, I noticed with the HDD usage-tracking in TaskManager that Chrome was still periodically scanning the HDD. "For our safety", of course. That's when I uninstalled spyware Chrome forever.]
Even though I always have Win10 set the USB ports as hot swappable, it still happens sometimes that when inserting a stick, I get the notice that it has problems and needs to be checked and fixed. Then about half the time, it reports that errors were found and fixed - half the time it says no errors were found.