Let's take only one and very clear example:
Any process can modify processor status register (or any equivalent register depending on the register naming and the processor in question). We have one bit telling are interrupts enabled or not. One process sets interrupts are not enabled any more. Then no interrupts will happen before next boot. The computer is frozen totally.
The operating system is helpless, because it can't recover without an interruption which could give a possibility to it to crash the oddly behaving process and fix the damage.