Apple has not officially defined or implemented any BYOD mode for any its iOS devices. Each iOS application of a non-jail-broken device has its own sandboxed file-system space, and there is no single system-level container that store all work-related apps and their data. Some MDM software claimed some kind of BYOD mode by implementing their own application-level container, but such containerization are not endorsed nor protected securely by Apple firmware.
Also, "Unsupervised" device is not equivalent to BYOD device. It is true that some enterprise-grade MDM policies (some restrictions, single-app mode, http global proxy, homescreen layout, etc. as defined by Apple in their "Configuration Profile Reference" document) are only available in Supervised devices, but such policies are not directly related to BYOD/non-BYOD use case classification. From my recent interactions with Apple Enterprise Account staff, Apple assumes all corporate customers needing serious enterprise-grade EMM implementation to use only DEP+VPP devices with supervised mode enabled. All legacy devices without these should be phased out a.s.a.p.