Regulation states that all commercial aircraft has to have a backup instrument system.
These systems are supplied from their own probes and runs of backup battery power; they are separated from the normal system to ensure the integrity of the backup. Exact design of system varies from aircraft model to aircraft model. The basics are the same: If the primary systems have failed the pilots are to use this last resort.
Pilots are taught to discard their own senses and look at the instrument. This is due to basic human anatomy. Without visual references the human body is really easy to trick into thinking that it’s in a different attitude than it’s actually in.
Due to the fact that pilots so relies on their instruments they are vital. There is a recorded accident with older generation of aircraft (mechanical, not computerized) where ground crew covered the inlets for the sensing systems with tape for aircraft cleaning and then forgot to remove the tape. The flight crew experienced faulty indications and the aircraft were lost.
When it comes to the electronic flight control system they are built to keep the aircraft from entering unsafe conditions. They operate with different levels of safety depending on how badly the aircraft is malfunctioning. There is more than one system and if one system detect a fault in the other it will let the pilots fly the aircraft without the computer restricting the pilots from entering an unsafe flight condition.
The problem is usually not the computers, as mentioned earlier there are backups and redundant system for all the vital systems that are necessary to keep the aircraft in the air.
The most common fault in aircraft accidents is a combination of small failures, bad weather and pilot overload (stress) with result in human errors.