A CPU is a very complex gate array which handles bothersome tasks such as synchronization (run conditions) and memory access, and presents you with a very limited set of instructions. All serial programming builds upon this very limited set of instructions, and the instructions have been thoroughly tested over the past 6 decades.
Not to say that CPU architecture or microcode is fail-safe, but the chance of your computer blue-screening because of a failure of your CPU is rather small.
Now, parallel programming (the low level variant, not the hijacked definition) is the art of "wiring" those gate arrays. A CPU is actually made using parallel programming, so all the safeties it presents for serial programming will not be present in parallel programming, as parallel programming does not use a CPU.
EDIT: the above is of course simplified, there exist multiple architectures, collected into more common instructions sets such as amd64, armhf, arm64, etc. but even the most barebone processing unit contains a lot of securities and nicities that parallel does not have.
I think you are misunderstanding me. Are you perhaps thinking about multithreading or multi core? Because some people have also started calling that "parallel", even if it is nothing like low-level parallel.
A CPU does not build upon a CPU, a CPU builds upon transistors which are collected into gates, and which can be assembled into the correct order using parallel programming.
EDIT: as an example, you do not actually need a computer to parallel program. Get yourself a box of transistor, some cable, and a soldering iron, and you can build some very rudimentary gate arrays, like a flip-flop.
This link might give a better understanding of our confusion.
EDIT 2: One could perhaps illustrate the confusion which this topic is often victim of as such:
Transistors are part of the hardware and are parallel programmed to form complex gate arrays called "Processors", which feature instruction sets used by machine code, which is made using assembly, which is called "serial programming", which enables high-complexity operations such as multi-core "parallel" programming.
I'm talking about the former "PGA parallel programming", and not the latter "multi-core parallel programming".