Unfortunately, this part is not available for purchase individually. Sony only
Typically, case parts such as this are not stocked in any quantity, even for current production models. Your tv is a 2011 model so all components are now discontinued.
The stand is available as a single unit, but not as individual components. Buying a new stand will cost you $225, which is obviously not going to be practical when you could buy a brand new tv for little more. I can certainly help with getting that part if you wish though.
If you want the plastic cover piece, you can watch for one on ebay, craigslist, etc, or check with local tv repair shops who may parting out a defective tv.
Other than that, your best option will be a generic/universal base, or to wall mount the tv. Here is an example: http://amzn.to/1jibnBH or http://amzn.to/1jibux9
Either of these options will work just as well at a fraction of the cost.