Let's read the GNU Coreutils source code

On this fan request roulette, we take a look at GNU coreutils, a collection of essential utilities for any GNU

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[tutacat]

No, SSDs are actually easier than hard drives to overwrite because there is less chance of the data being recoverable even on one pass. You could just write zeroes to that location and it would be fine (just use FStrim after deleting a file for example)
The wear levelling algorithm maps the same ATA location to the same physical location, just that the mapping is random.