I thought the 80286 had 32-bit protected mode, but it was badly implemented (the only way to get back to real mode was a reboot), so they fixed it with the 80386. Unless, are you referring to “unreal mode”?
No, most people forget about it (I had to be reminded by the above comment), but the 80286 did have a 16-bit protected mode. Quoting Wikipedia (https://en.wikipedia.org/wiki/Protected_mode): "[...] Acceptance was additionally hampered by the fact that the 286 only allowed memory access in 16 bit segments via each of four segment registers, meaning only 4*2^16 bytes, equivalent to 256 kilobytes, could be accessed at a time. [...]"
