By default, Stinger quarantines to C:\Quarantine\Stinger.
This directory structure is then left behind on close.
Although there is an option within the program to change this location, I can't find where that data gets updated, so I can't offer any ideas on how to change it permanently, other than to do a DirectoriesMove on the directory structure.
The empty directories being left behind is fixed in the current release of McAfee Stinger Portable (via the launcher as long as you run it a second time as instructed on launch). Any quarantined files will naturally be copied there as they should since they are specific to the local PC (not the portable app) as indicated on the app's homepage.
Sometimes, the impossible can become possible, if you're awesome!