Back when CCPs had to achieve reauthorisation under EMIR, their segregation offerings were a subject of much discussion and jargon. One key offering that was floated was the idea that your assets are held in an account over which you have joint control with the CCP, rather than held in an account for the CCP solely.  The idea being that should the CCP default or be unable to service your requests to access your assets, you would have the possibility of moving assets out of your cover account. In the event that the CCP is still operative, assets in such an account may be held by the CCP, so not open to movement, and instructions given to the custodian to represent the CCPs interest in those assets. 

SwapClear has joined the physicall segregation party with their own offering, details here: http://www.swapclear.com/service/customer_protection_under_emir.html

To paraphrase their PDF, these are the key benefits:

• Keeps your assets totally separate from any other client or your intermediary (FCM or CB)
• Means asset deliveries are direct into your account, not via your intermediary
• Means you can still deliver assets to the CCP should your intermediary itself be in default
• Enables substitutions directly by your firm
• The securities remain under your title

Other CCPs have similar offerings, although finding details on the physical segregation models can be tricky:

• http://www.eurexclearing.com/clearing-en/about-us/news/otc-clearing—client-asset-segregation—options-for-the-fund-manager/1111152
• https://www.theice.com/clear-europe/client-clearing
• http://www.cmegroup.com/europe/clearing-europe/risk-management/customer-protection-and-segregation.html