All that has been said on this thread supposes that the hard drive is still readable and writable.
But the original post stated this was a failed drive. Then you might not be able to dd if=/dev/zero of=/dev/sdx .. or whatever else. You would be stopped by bad sectors. Or a hard drive might not be accessible at all through the computer interface. I heard something that sounded like a modem dialing, but had no such modem. Going around with my eyes and ears led me to determine that it was a hard drive whining in an external eSATA enclosure, no longer recognized or accessible from the computer. That was a Western Digital Green 3 TB hard drive that replaced, under warranty, a WD Green 3 TB hard drive that developed bad sectors. Fortunately I had no confidential data on that hard drive. So everything in this thread says nothing about if the hard drive failed due to a mechanical problem. Then the data could not be overwritten by ordinary means, but could still be read by techniques such as used by Drive Savers. Tom