It's certainly possible. A "quick" format only rewrites certain structures on the disk but leaves most of the data unchanged. And you should never overlook the possibility that a clever virus may be intercepting the normal Operating System commands. "Format" may not be doing what you expect it to.
Simple answer is yes, yes they can survive.
However it is unlikely, it's more likely that your HDD may be faulty if you are still experiencing issues after a format or that any virus may be on another partition of the same drive.
Don't expect to find anything useful on the drive after that, not even a partition table. Just make sure you don't specify the wrong drive for "of" or you can kiss your good data goodbye as well. If a virus happens to hijack dd, well, you should probably worry about your flash drive later.
Thank you for the answers.
I thought virus couldn't get through a format. I now understand it can. That makes it difficult to get a safe
So what if you fill up the usb stick with data files after deleting the usb stick? That won't work, because
the virus can be written in a way, so it actually doesn't get overwritten?
To clearify, I'm not asking this quistion because I suspect I have a virus problem on a usb stick. It was
a general question, whether you can make a usb stick, that you reason not to trust, safe again.
But it seems you can't.