I have a Motorola XT1080 (also known as droid maxx) from verizon, and it is running android version 4.4.4. Is it possible to root this device, and if so, how do I do this?
Try to unlock the bootloader with Sunshine S-Off then use kingo rooting tool. Or try Kingo first as it's free but Sunshine will test your device to make sure it can unlock the boot loader. If so, it will cost 25$ but you have better odds of getting root with the boot loader unlocked.
I have the same phone, I lost root and could not get it back with traditional maxx rooting methods so I unlocked my bootloader with Sunshine then rooted with Kingo but I did all this on android 4.2.2 so it may or may not work on 4.4.4 (please comment on this answer with your results if you try this).
Another program like Kingo is Root Genius.
I have a XT1080 running 4.4.4 KitKat and did have some luck using king root ( not a typo Kingo root is a separate app ) then root checker to verify it was actually rooted and to also install busy box. Either because of my lack of knowledge or actual conflicts caused by the programs I kept getting error messages and finally did a factory reset out of frustration. It's something to try if you're familiar with rooting and tweaking the settings for performance.
P.S. Almost forgot I used device controller from the play store to do my phone tweaking
Well, that's weird I would say you would have got the device rooted using Framaroot, double cross check if you are using the latest version of the Framaroot to root your device?? I somewhere doubt that you are trying to do the same with older version of the Farmaroot, anyway I think it would be better for you to try doing that again using the latest version of Framaroot 1.9.3 over here.