I've looked into this before, and as far as I could determine, it is upto each application itself whether or not it has the ability to save the current state (Firefox especially).
I think some kind of standby or suspend ACPI option like in windows is the best idea, as this simply saves the current CPU and RAM status to a large dump file (swap file essentially, yet not as gracious), and then loads the current state the next time the machine is booted.
Hope this helps in some way.
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