EoD did testing on Sapphire R9 380X Nitro, details at
https://gist.github.com/EoD/2baa78b81e233218a59c and copied below:

Booted with DVI-D-0 + HDMI-A-0
Both displays work

Booted with DVI-I-1 + HDMI-A-0
Both displays work

Booted with DVI-D-0 + DVI-I-1
DVI-D-0 shows output, DVI-I-1 stays blank  (via xrandr)

Booted with DVI-I-1 + plugging in DVI-D-0 after boot
DVI-I-1 shows output, DVI-D-0 stays blank  (via xrandr)

Booted with DVI-I-1 + plugging in DVI-D-0 after boot + removing DVI-I-1: 
DVI-D-0 stays blank  (via xrandr)

Booted with DVI-I-1 + plugging in HDMI-A-0 after boot + removing DVI-I-1 +
plugging in DVI-D-0:
HDMI-A-0 shows output, DVI-D-0 stays blank (via xrandr)
When switching to a virtual termina, HDMI-A-0 goes blank, DVI-D-0 shows output