Do Dual CPUs Provide Fault Tolerance?
Solution 1:
In a normal dual-socket system, no, although there are servers that do permit hot-swapping of processors and RAM. So these things do exist, but they're at the very, very high-end of the market.
It's not really a big deal - of everything in your server that can fail, the processor is right on the bottom of the list, next to those little brass risers that hold the motherboard off the chassis.
Solution 2:
Talking about x86 commodity hardware, if a system is running and a CPU fails things will grind to a halt normally. However the system will function fine after a reboot, albeit somewhat slower.
Multiple CPUs mostly are there to have parallel processing, not really for fault tolerance. But it's nice to have a system that still boots would a CPU (or more) fail.
I would say it's bit more likely your CPU fails than Mark Henderson suggests, but it still is very unlikely. In my experience mostly it happens when the system frequently overheats and shuts itself down (that's quite easy in a badly airconditioned office server room). The CPUs don't tend to like that a lot.
Of course if you had a nice IBM mainframe or similar, hot swapping a CPU (board) is "easy" enough.