Based on [1], thread running inside a critical section cannot be preempted by other threads on the processor. That means deadlock won't happen since nested critical sections are still run by the same thread until it exits the outermost critical section.

Thread halting is a not problem as long as it resumes to complete the critical section. Interrupt can happen. The interrupt state is saved to be handled later, the thread resumes to finish the critical section, and then the saved interrupt is delivered to the interrupt handler. The scheduler is interrupt driven anyway.

Thread killed while inside a critical section can be a real problem, as the critical section is not released, preventing other threads from running on the processor. I'm not sure how Linux handles it, whether it would clean up the critical section when the thread is killed or the killing waits until the critical section has finished.

[1] https://en.wikipedia.org/wiki/Critical_section#Kernel-level_...