Random example: I once worked on a debug where you were not allowed to send zero length packets due to a known HW bug. Okay fine, work around in SW. Turns out there was an HW eviction timer that was disabled. It was connected to a counter that counted sys clk ticks. Turns out it was not disabled entirely properly due to SW bug, so once every 2^32 ticks, it would trigger an evection, and if the queue happened to be empty, it would send a ZLP, which triggered the first bug (hard hang the system in a way that breaks the debugger). There were dozens of ways that could hard hang the system, this was just one. Good luck debugging that in two days.

We had one where data, interpreted as address (simple C typo before static analysis was common) fell into an unmapped memory region and the PCI controller stalled trying to get a response, thereby also halting the internal debugging logic and JTAG just stopped forever (PPC603 core). Each time you'd hit the bug, the debugger was thrown off.