Can a faulty Micro-USB cable cause damage to your device? Hardware damage caused by USB Type-C cables by drawing too much power has been widely reported:


https://www.howtogeek.com/240777/watch-out-how-to-buy-a-usb-type-c-cable-that-wont-damage-your-devices/  
http://www.theverge.com/2016/2/4/10916264/usb-c-russian-roulette-power-cords  
http://www.pcworld.com/article/3002064/computers-accessories/beware-bad-usb-c-cables-google-engineer-warnswhile-naming-names.html  
http://gizmodo.com/cheap-usb-c-cables-could-kill-your-phone-or-laptop-1757115350
http://www.androidcentral.com/usb-c-problem-isnt-going-away-anytime-soon


Is Micro-USB affected?
Root of the problem is non adherence to standards and not type C as a class of faulty cables. 

The damage caused specifically relates to :


poor adherence of standards to the extent of being non standard
Using a wrongly rated resistor by one plus
in their products, which fried other devices connected to such cables


Benson Leung is a Google Engineer who carries out extensive testing of practically anything related to type C, which you can read on his Google Plus

If you use any non standard product, you always run the risk of damage / poor performance. This is equally true of micro USB cables, though I haven't come across such bad press for micro USB ( barring chargers of spurious quality)