Processors, methods, systems, and instructions to determine whether to load encrypted copies of protected container pages into protected container memory

A method performed by a processor of an aspect includes accessing an encrypted copy of a protected container page stored in a regular memory. A determination is made whether the protected container page was live stored out, while able to remain useable in, protected container memory. The method also includes either performing a given security check, before determining to store the protected container page to a destination page in a first protected container memory, if it was determined that the protected container page was live stored out, or not performing the given security check, if it was determined that the protected container page was not live stored out. Other methods, as well as processors, computer systems, and machine-readable medium providing instructions are also disclosed.