I'm having the same problem on Xubuntu 16.04 with lightdm & xfce4.

Video board is "NVIDIA Corporation GK107 [NVS 510] [10de:0ffd] [10de:0967]", with 3 monitors connected via DisplayPort.

The monitors are on a single power strip.  When I leave for the day I lock the X session (ctrl-alt-L), then turn off the power strip.

Next day I noticed that X has tried to dump core about 400,000 times (seen in /var/log/apport).  /var/log/Xorg.1.log.old ends with:

[942209.134] (EE) NVIDIA(0): Failed to assign any connected display devices to X screen 0. 
[942209.134] (EE) NVIDIA(0):     Set AllowEmptyInitialConfiguration if you want the server
[942209.134] (EE) NVIDIA(0):     to start anyway
[942209.135] (EE) NVIDIA(0): Failing initialization of X screen 0
[942209.136] (EE) Screen(s) found, but none have a usable configuration.
[942209.136] (EE) 
Fatal server error:
[942209.136] (EE) no screens found(EE) 

/var/log/Xorg.1.log is normal -- it represents the 400001st attempt, which succeeded because I had turned the screens back on.

So I created /usr/share/X11/xorg.conf.d/10-nvidia-no-monitor.conf with:

Section "Screen"
    Identifier     "Screen0"
    Device         "Device0"
    Monitor        "Monitor0"
    Option         "AllowEmptyInitialConfiguration" "True"
EndSection

and Xorg :1 no longer dumps core -- now it just comes up blank.  :(

So now I can power my screens back on, flip to ctrl-alt-F1, login on the text screen, kill the dysfunctional :1 server, a new one starts up successfully, then I can unlock and return to my :0 session.  Is this an improvement?  Maybe -- I don't like the idea of the system churning along trying to dump core 5 times a second, all night or weekend long...

But wait, how does this relate?

Well, if I *don't* lock, just turn the monitors off, then my Xorg :0 session hangs.  Turning the monitors back on, they're just black; after a few seconds they flash "entering power-save mode".

/var/log/Xorg.0 shows that before power-off, each of the monitors was "connected", like:

[942221.128] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-4): connected
[942221.128] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-4): Internal DisplayPort
[942221.128] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-4): 960.0 MHz maximum pixel clock

When I power them off, this becomes:

[946263.004] (--) NVIDIA(GPU-0): DFP-4: disconnected
[946263.004] (--) NVIDIA(GPU-0): DFP-4: Internal DisplayPort
[946263.004] (--) NVIDIA(GPU-0): DFP-4: 960.0 MHz maximum pixel clock

-- repeated several times over about 1/4 second; then:

[946263.279] (II) NVIDIA(0): Setting mode "NULL"
[946263.408] (II) NVIDIA(0): Setting mode "NULL"

(which I think represents what it's done to 2 of the 3 monitors); then, after I power them back on,

[946313.566] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-4): connected
[946313.566] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-4): Internal DisplayPort
[946313.566] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-4): 960.0 MHz maximum pixel clock
[946313.566] (--) NVIDIA(GPU-0): 
[946313.566] (--) NVIDIA(GPU-0): DFP-5: disconnected
[946313.566] (--) NVIDIA(GPU-0): DFP-5: Internal DisplayPort
[946313.566] (--) NVIDIA(GPU-0): DFP-5: 960.0 MHz maximum pixel clock
[946313.566] (--) NVIDIA(GPU-0): 
[946313.573] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-6): connected
[946313.573] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-6): Internal DisplayPort
[946313.573] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-6): 960.0 MHz maximum pixel clock
[946313.573] (--) NVIDIA(GPU-0): 
[946313.580] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-7): connected
[946313.580] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-7): Internal DisplayPort
[946313.580] (--) NVIDIA(GPU-0): DELL P2715Q (DFP-7): 960.0 MHz maximum pixel clock
[946313.580] (--) NVIDIA(GPU-0): 
[946313.640] (II) NVIDIA(0): Setting mode "NULL"

-- in which it has set mode "NULL" on the 3rd monitor even though I just turned it *on*.

After this, nothing good happens until:

[946785.125] (II) NVIDIA(0): Setting mode "DP-4: 1280x1024 @1280x1024 +0+0 {ViewPortIn=1280x1024, ViewPortOut=1280x1024+0+0}"

-- in which I had flipped to tty1 (text) and run:

   $ sleep 3; DISPLAY=:0 xrandr --output DP-4 --mode 1280x1024

-- then flipped back to tty7 before the `sleep` ran out.  Running it without a delay failed (I forget the error message) -- it was necessary for tty7 to be active when the command ran.

SOMETHING, I think either lightdm or xfce4, is making wrong decisions about driving the monitor with XRANDR protocol.  Once the monitor has "disappeared" (been turned off once), it decides it's permanently gone, fails to notice when it "reappears".  The nVidia driver might also be partially at fault, I can't really tell.