PE=0 Dbit=0 (un)Real Mode
PE=0 Dbit=1 Forreal Mode
PE=1 Dbit=0 Veal Mode (BKA "286 task")
PE=1 Dbit=1 Protected Mode

Yes Forreal Mode works. I have some code, but it's in my own assembler in Bash. The thing is, you have to handle interrupts in 8086 mode, i.e. you have 66/67h IRET.

Where it might be useful is realtime. No big task switch latency. So for example, you could have a unix-like OS, with real protected mode for guest users, but let the "root" user operate in Forreal mode for video and whatnot. Syncing audio to other stuff might benefit quite noticeably, I suspect.

Hmm, it seems like he implemented the same thing that I called the unREAL mode in my implementation (fasm for DOS and the kelvar example use this mode). This was really a lot of fun implementing it - I did it with help of Leonid Petroff, he was a great comrade in DOS programming. Before I realized that it is possible to relocate IDT for 32-bit code, we had to use a hybrid interrupt handlers, which were able to detect, whether they are executed as 16-bit or 32-bit mode, and behave accordingly. I'm afraid I don't have the copy of those first implementation, but from my memory the beginning of interrupt vector looked like:

Code:

use16 
mov cr3,eax ; bitness-independent instruction; CR3 used as a safe storage, as it's unused in real mode 
mov ax,0 
jmp short int_16bit ; in 32-bit the "mov eax" instruction eats this two-byte jump 
use32 
; here we know we're in 32-bit code, so we have to switch back to 16-bit before calling DOS/BIOS interrupt handler 
; ... 
int_16bit: 
; here just restore EAX from CR3 and jump to the original interrupt handler
    

Of course with separate interrupt tables for 16-bit and 32-bit mode this became much simpler and such implementation you can see in fasm.