How to bypass a MCU if it fails?
You'll need to define what "MCU failing" means. In a generic application, the most likely faults are probably either the firmware going haywire or the part getting shorted/fried/losing solder connection etc, all of these risking MCU hang up.

Normally you'd protect against such through digital logic, by having the MCU repeatedly feed an external watchdog circuit, such as a monostable multivibrator (example) or similar part that needs to be repeatedly refreshed with a signal. 

Then let the MCU's transmitted PWM go through a fast-enough switch/mux. As long as the MCU keeps feeding the external watchdog, the external watchdog will enable the MCU PWM output through this switch. Otherwise, it will pick the input PWM and route that one to the output instead.

A design like this could be sufficient even for safety/mission critical purposes, though you might have to walk some extra mile in risk assessment. For example, when this fault happens it might be important to alert about the system having entered this "failsafe/limp home" mode. And high integrity systems may require multiple MCUs supervising each other etc.