Final answer:
The Authorized Program Facility (APF) is the z/OS feature that allows selected programs to reside in special libraries, giving them the ability to access sensitive system functions in z/OS.
Step-by-step explanation:
The z/OS feature that allows selected programs to reside in special libraries and access sensitive z/OS system functions, such as running in supervisor state or executing privileged instructions, is the Authorized Program Facility (APF). APF is a crucial component of z/OS security, as it provides a mechanism by which system administrators can control which programs are allowed to perform functions that would normally be restricted. Programs that require this level of access to perform their intended functions must be located in an APF-authorized library. Access to these libraries must be carefully controlled to avoid unauthorized use of privileged instructions.