To be honest, I suspect the problem is with the MSI afterburner itself. these programmes are often not suitable for all cards/vbios and interfere too much with the drivers. All of them; EVGA, MSI etc. are the worst i tried. They are not suitable for my actions for example. None of them!
More blatant spreading of false information

There are probably millions if not billions of people who have used MSI afterburner on a whole range of new and old cards and worked perfectly fine. Ive heard of RTSS interfering with 3D apps once in a blue moon but those are extremely few and far between and never to the point where it would crash a PC outright in the middle of gaming. If the OC is too high then that is user error not a problem with the software that
YOU used to raise the clocks.
You make so many claims about how the app does bad things but back none of them up, Your information isnt even correct either MSI Afterburner has nothing to do with the vbios. It uses the driver to set the clocks.
If its not suitable for your needs --
dont use it. But dont tell other people to stop using it because it didnt work for you.
If the card is very old, the transistors or the silicon may well be showing their age.
Nothing lasts forever.
I suspect a mixture of everything, but primarily the fact of intervention by a third-party programme.
you can try the NVIDIA inspector.
i've had the best experience with it. it's not a programme that has endless setting options, but it is explicitly tailored to NVIDIA and delivers quite good results. i am very satisfied since i use this tool
If the transistors or the silicon is old Nvidia Inspector isnt going to tell him this. Neither is MSI Afterburner.
If the system is shutting down during gaming then it could be anything. But definitely a hardware issue...
Having unstable or ram your mobo doesnt like can cause things to crash.
Having an unstable or dying CPU can cause a system to crash or thermally shut down because its getting too hot.
Having a bad power supply can also cause a system to crash. OP states he has a 400w but he doesnt state which brand of 400w. Not all power supplies are made equal. It could be a
'400w' $10 power supply he bought off aliexpress.
Having a bad motherboard can also cause crashing
Having bad Hard drives/SSDs can also cause crashing -- but probably more random crashing and not just when gaming.
Im guessing its not the board, ram or the CPU because it was probably working for the OP before he put the 560 in so by process of elimination. Im going to say either the power supply is weaksauce or the 560 is bad because it was dropped
Try the 560 in a different PC or test your PC with a different GPU or swap your Power supply out for a better one. Trying the 560 out in a different PC would be my first step as that takes it out of the puzzle and you know that the card is not faulty which means its probably the power supply.
@Kk84 -- you dont need an 800w power supply. very few people do. Even when i had GTX680s and 970s in SLi with an older 3930k@4.6Ghz setup my PC barely peaked 700w at all. My current system doesnt even pull 400w but i am very modest when it comes to how crazy i want my Frames per second to get.
a good 500-650w from this list here Either from Tier A, B or C will get you a solid capable power supply that can probably run upto a 3070. Obviously the higher the tier the stronger/better the unit for its class -- Buying a unit from Tier A or B isnt required but should be better quality should you decide you have the money to go down that route.