Edit: I am leaving the answer for informational purposes so that any future reader can see what was tried.(comments include additional info) It was discovered in the course of trying to resolve this that the desired function was removed. If any reader knows different please let me know

While the exact behavior is not possible, nearly the same thing can be accomplished by enabling hibernation. Be aware, however, that some systems do not support hibernation(the reason it was removed as a default option), so before you add the needed file in the following link Be sure to test it using the terminal command

How do I hibernate my computer?

for potential issue (and some workarounds) for hibernation/suspend see:

Why won't my computer turn back on after I suspended it?

I am using this question and answer for reference, but the answer is slightly different as the program name and the location of the settings have changed so I do not believe that the above question is quite a duplicate of my source Hence, I will post a new answer.....

Q:How do I make a program auto-start everytime I log in?>> A:To make a program start with Ubuntu:

The program you need used to be called gconf editor but is now called dconf editor

You can install it by installing the program dconf-tools

After you install it you can use the dash to open it as Dconf Editor.

There is a tree on the left of the window that you can use to navigate to the correct settings page.

The path is: org>>gnome>>gnome-session

You will then be presented with a screen that looks like this:

Where the mouse pointer in the screenshot is is the setting that you want to select by checking the box.

This should then save the current running programs and start them again when you reboot. The settings are saved when you check the box, there is no save button that you need to click before closing dconf editor.

Warning: This will only save a list of the applications to restart the next time you reboot, it will not save any unsaved statuses (i.e. any unsaved documents) on shutdown and all unsaved work will be lost.(Likely an unneeded warning but better to include it anyway)

If you want to disable this you can do it by simply unchecking the box.

As my source answer states, this may significantly slow down your boot if you have a large number of open programs when you shut down....I would also add that Firefox does not like it when you shut down your computer when it is running, it will do not damage but it will entirely wipe out your internet cache(saved webpages), but it will leave your cookies intact---if you have your cookies set to delete when the browser closes, you would need to verify that the cookies was removed, I'm not sure if they will be or not. I can give no guidance on Chrome/chromium, I use neither one.....

I have to add a caveat to my answer, I did not try this to verify, but, I have no reason to believe that it will not work. My source answer was an accepted answer with 29 upvotes and the settings are still available, albeit in a different location......