I have an R9 380 connected to two HP wide screen HP displays via DVI cables. The mobo is Gigabyte Z170X gaming 7 with a stock i7-6700, not overclocked, and 32 gb RAM. Without the R9 380 everything works perfectly. OS is a clean install Win 10, not an upgrade. I have done a wipe and clean install of the latest hot-fix Crimson drivers as of today, 5/1/16, in an unsuccessful attempt to overcome the following problem.
When the system is set to shut off the displays (but not yet sleep the CPU), the displays do go dark. But the system gets into a loop where it just keeps beeping every 20 seconds or so, and never goes to sleep. Clicking the mouse wakes the displays. However, any window open on the 2nd monitor has moved to the primary display.
This problem does not occur when the R9 380 is not in the system. It does not occur if the monitors are connected to the mobo HDMI and display mini-port outputs. This mobo has Intel graphics on board, which work fine but are slow for my purposes. It's driving me nuts. The only workaround is to leave the displays on until the system goes to sleep.