Hi, and welcome!
My first thought is this is definitely due to lack of resources, RAM in particular.
This is pretty much what would happen when the system runs out of memory: hang, and then the Linux kernel starts shutting off processes in order to be able to continue to function. At one point, the virtual machine gets destroyed freeing the resources that are needed to restore the system to a working state.
I don't disagree, but consider that the base OS needs resources for itself as well, including the network stack that is handled outside of the VM, as does the virtualization layer itself. You're probably running a little too close to the edge.
Something that will help with this is enabling ZRAM. This compresses the RAM used by the system so that the same amount of memory is used more effectively, at the cost of increased processing. But probably well worth it in this case.
Not a problem at all. For future reference, try to edit the post instead of making multiple new ones, just to stay more organized and make searching easier. And as an aside, when pasting output from the terminal it's preferable to wrap it in triple backticks (`) to format the text a little nicer, for example:
gintautas@Gintautas-ThinkPad-Edge-E531:~$ lsmod | grep kvm
kvm_intel 487424 0
kvm 1409024 1 kvm_intel
irqbypass 12288 1 kvm
Don't worry about it now, it's not a big deal, just something to consider for next time.