Forcing server as idle as possible (all OSes, but possibly illumos too)

Running on top of a hypervisor like Xen or VMware gives you the option of taking snapshots including RAM, and even suspending the VM indefinitly, thus achieving what you are asking.

The problem you describe does sound like something you could avoid by taking a different approach - like avoiding keeping local state on the server in question. As you haven't shared anything about the environment you operate in or why you need this setup, it does sound overly complicated and prone to failure.

Edit

The details you give don't elaborate on the "Why".

In some such cases, the server must be kept on to preserve some inner state: it cannot be powered off, nor restarted, but at the same time, it must be put in a state as idle as possible, trying to keep it on until tech arrive.

Why?

If you need this to provision a replacement, this is what configuration management is for (puppet/ansible/cfengine + something like Foreman)

If you need this to continue operation after replacement (e.g. application state), try to keep it off that box if possible.