So, after the heir's assassination you enter a period of increasing instability with the emperor being faced with multiple opportunities to either go paranoid/tyrant in an attempt to crush internal opposition, all of which extends the duration of the situation (and in principle could go on forever) or accept the opposition as being legal, or excusable, or not bad enough to repress. You can also try to crush the opposition by enacting decisions on planets, killing egalitarian POPs and forcibly converting to authoritarians, which is also the acts of a tyrant.
The default duration is 180 months, but how long time it takes depends greatly on your choices.
This continues until one of three things happen:
- The situation terminates unnaturally - e.g. Luminary dies somehow. Ignore this one.
- The situation terminates naturally by reaching the end, where the instability forces everybody to the negotiation table on the brink of civil war
- The emperor completes the Total Crackdown agenda, forcing negotiations from a position of strength. (Which is easy to do in time if you have an expanded high-level council, but can be harder if your empire hasn't invested in leaders - though of course you can extend the time you are in the situation by being a paranoid tyrant, should you so wish (which you just might, if you are bloodyminded enough)
So the situation had ended and it is time for the parties to negotiate. What to do with the imperial rule that nobody signed up for in the first place? What about the people's grievances?
Option 1: Negotiations after situation completed naturally
Basically, if you were only a little bit a paranoid tyrant (max 5 stacks) you lose the trait and are considered a good ruler. If you have have 5 or more stacks you are considered a bad ruler.
If you were a bad ruler, and you never took the reformists side, then the demand of the opposition are harsh. Your opponents will want to revert to dictatorial rule, reverse ethics, and, if you don't have shadow council civic, want to get rid of aristocratic elite and merchant guilds civics (if you have them) and replace them with shadow council civic.
If instead you were a good ruler, they are fine with imperial rule... so long as it is one which guarantees them some constitutional freedoms. If you don't have efficient bureaucracy civic, they'll want to replace aristocratic elite and merchant guilds with that instead if you've got them. More power to the people, less to the leeches.
In addition they want more of a say in running the council (increased worker power modifier), and want to get rid of Slaver Guilds and Dystopian Society if you've got them (to be replaced by Philosopher King, Mining Guilds or Efficient Bureaucracy).
Finally, if the main species has stratified society, academic privilege, or subsistence living standards, they want standard living standards.
The terms for a bad ruler are probably enough to make the player look at civil war as an attractive alternative, whereas for a good ruler they might be annoying, but easy to deal with.
Option 2: Negotiations after Total Crackdown
Here too, you get considered a good ruler if you were only a little bit a paranoid tyrant (max 5 stacks) and you lose the trait. If you have have 5 or more stacks you are considered a bad ruler.
First, the people want more power. How much depends on other factors, but always half what you'd have had in the equivalent situation the first scenario. Best case you might end up with 7.5% increased worker POP power. The horror! 
They also want to get rid of Slaver Guilds and Dystopian society if you have them in favour of Philosopher Kings, Mining Guilds, or Efficient Bureaucracy.
And living standards set to standard if they are worse for the people, just like in option 1.
And that's it. If you are a benevolent autocrat, who doesn't let grief over the death of the heir turn into outright paranoia and persecution, and doesn't let the situation spiral out of control, but are willing to compromise with people seeking constitutional guarantees and limits, and if your society isn't a hellhole in the first place, then you can end the situation with 7.5% increased worker power and granting them standard living conditions.
You'd have to be a fool not to take this if it is available. (Or a really determined roleplayer, who on the one hand did not want to tyrannically oppress people, but on the other hand was dead set against the people having rights or a full stomach.)
Option 3: Civil War
This is always an option, and if you've been a bad ruler during your grief, or you don't want your people to have a say because they should live under your iron fist, it might be your best choice.
Option 4: BLOOD
So, you've been a paranoid tyrant. You extended the period of madness, cracking down on the innocent and guilty alike time and time again, making your people well and truly hate you. (Requirement: 10 stacks of Paranoid Tyrant or more)
And now the traitors who dispute your just rule are trying to negotiate with you? THE FOOLS. You can't help but giggle madly at the thought, that they thought you were earnest about negotiations. KILL THEM ALL! And their families. And friends, neighbours, and pets. Better kill the potted plants too. Let the streets run red. And green in case of the plants. Better kill the gardeners too.
Gain another 5 stacks of Paranoid Tyrant on top of the 10+ you gained during the situation, and gain 8 stacks of Luminary growth too, as everybody is in awe of you - and better yet, terrified. NOW WHO IS LAUGHING? MUAHAHAHA.
This path avoids civil war too.
Option 5: REVOLUTION!
Kills the Luminary and lets you take control of the rebels as an idealistic foundation democracy in the civil war.
