macOS High Sierra – Where to Find Secure Empty Trash Option

You will not be able to erase the entire contents of the disk, format/remove the partitions (securely or otherwise) while the volume is mounted. Because of this practical limitation, without having your original installation disc from which to boot into Disk Utility, you're stuck with a system that is in a vulnerable state to sell. While you can create a throw-away admin account from which to securely delete your user profile, OS X still splatters information, such as network connections, all over the place.

As Buscar correctly stated, the resale value on what I would I imagine is a circa 2008/2009 system is low enough already WITH all the original discs. Without them, the possibility of selling is fairly low. The biggest reason for this is that you need the original discs for running diagnostics. Apple Diagnostic software is mated to the particular hardware.

Although Apple no longer supports these systems and, therefore, does not sell replacement DVDs, you can purchase recycled installation DVDs from ifixit.com. I purchased original Leopard install DVDs from iFixit for an Early 2008 MacBook4,1 that was gifted to me without discs. Highly recommended.

With the correct DVDs, you can securely erase the HDD and let go of the system with complete confidence. Alternatively, you may consider simply replacing the HDD in the system with a new one and destroying the one you've been using. Your out-of-pocket cost is probably around the same, but the original DVDs would likely net you a higher resale value.

Mavericks does not enable encryption (FileVault 2) by default -- it may (if several requirements are met) offer to enable it during the initial setup process, but it's not the default. Also, even if the volume is encrypted, insecurely deleted files can still be recovered by someone who knows an enabled password (usually any user with an account on the computer).

So, I'd consider Secure Empty Trash to still be relevant (in at least some situations) in Mavericks, even when FileVault is enabled.

However... Secure Empty Trash is not really enough, and hasn't been for a long time. In many apps, when you edit a file, it saves changes by deleting (insecurely) the old file and writing the new version. Securely deleting one version still leaves any older (deleted) versions lying around the disk. So you really need to use the Erase Free Space feature in Disk Utility to go back and make sure they're overwritten.

Oh, and neither Secure Empty Trash nor Erase Free Space really work right on SSDs, just on magnetic HDs. So ... it's complicated.