Yes and no.
I don’t know where on disk the files are stored. Fortunately, that doesn’t matter, since you can use Windows Defender itself to manage the contents of the vault. Even better, you probably don’t need to do a thing.
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Vault and quarantines
The “vault” is the location where anti-malware programs like Windows Defender place files identified as malicious or suspicious. It’s also frequently referred to as “quarantine”.
Depending on the specific threat, the anti-malware program moves malicious files to this safe, quarantined location in case you need to recover them later. Not all discovered threats may be moved, however; some may be deleted immediately.
There is no standard vault location. Each program sets up and uses its own strategy for managing its vault.
Managing Defender’s results
Double-click on the Windows Defender icon — — in the taskbar to open the Windows Defender Security Center. Click on Virus & threat protection.
Click on Threat history. This will list current issues and quarantined items if any are present.
Click on See full history.
This will list recently discovered issues that have been dealt with. If you’re experiencing false positives, you can also indicate that specific threats are to be allowed (by clicking the down-arrow to the right of an item listed, and then the “Allow” button, not shown).
Manual action not required
One of the phrases to note in the dialog above is “They will be periodically removed” in the quarantine section.
The implication is that you do not need to empty the quarantine yourself; it’ll be handled for you. They only time you really need to visit these settings and history is if you’re curious, or if you’re trying to address a specific problem such as a false positive.
Windows Defender is, for the most part, completely self-sufficient and self-maintaining.
Updated for Windows 10