I have a system that boots from a solid state disk. How can I make it immune to improper shutdowns? I can also switch to a distribution having this feature. I can choose between Ubuntu, Redhat, and Fedora (or derivatives of these distros).
No system is immune to improper shutdowns.
That's why you have UPS that when connected to a system informs it that the main power is no longer available and the system will start a controlled shutdown. (Assuming that has been configured for it).
Although the previous info warns against power loss nothing stops a user of pressing the power off and shutting down the system in a improper way.
What you have nowadays is better automated recovery methods that "reduce" the problem that you might have when performing a improper shutdown.