How old is that drive?
What format is it in?
The new folder is created at the start of the transfer so it does not happen after the error code message.
If you only use that thumbdrive on a Mac, then consider formatting it to OS X Extended, far more stable than FAT.
Try this. Create a folder on the desktop. Open the data folder on the Thumbdrive and drag the contents into the folder on the desktop.
Should be no problem, as usual.
Now open the folder on the desktop and drag the contents onto the folder on the Thumbdrive. You should get a warning about an existing file, say replace and all the files should be transferred.
It's a work around, if it works, until you can reformat the thumbdrive.
They don't last forever.
I have a new MacBookPro, 320HD, 2.66GHz Intel Core 2 Duo processor, with Snow Leopard. I have always put my thumb drive into a slot and transferred my data to the desktop so I can work on it. Only with my new computer does the following happen. After working on any files, I drag them back to the thumb drive. I keep getting the following message, "The Finder can't complete the operation because some data can't be read or written. (Error code -36). It will then create a new folder just like the one I'm transferring to the thumb drive, only without any files. I can then transfer single files to the new folder, but only if they aren't in a folder. So anything in a folder will not be transferred until a new folder is written on the thumb drive and then I have to transfer single files until everything has been moved over. Never happened before, hope someone can help.