Are "permanently" deleted files always stored on the same partition on an HDD?

Or is it possible that it gets sent to the unallocated part, or another partition, of the HDD?

Asking because I deleted a file the normal way by accident when I wanted it shredded instead, and I want to know if using "wipe free space" on that partition with a file shredding application would shred the file to make it unrecoverable. I can't select the unallocated part of the HDD with that application

Edit: LUKS encrypted Btrfs partition. It's a …

accident asking file files free hdd privacy space