So anyway, the premise is this: A billionaire dies. An investigation shows that he was murdered. While the investigation continues without yielding any good leads, another very rich person gets killed. Different MO, so no direct link to the first case, but it's suspicious.
After yet another murder, police has to face the fact that a serial killer is out and about. The victims are always filthy rich, and never is anyone close to the victim a collateral. No families, no employees, no security professional is ever harmed. Police are stumped as to how the killer manages to do it.
Society's reactions are interesting. News are full of this spectacular case. You don't have serial killers in real life all that often, and the victims are all famous or at the very least well known.
The official view, of course, is "murderer bad". But among close friends, or anonymously on the internet, people start stating what they believe everyone is thinking anyway: Good riddance. Billionaires are parasites to society. The world, society, nature, and climate are literally better off without them.

Meanwhile, The Rich People are getting anxious. Reactions differ and can largely be divided into four groups.

Those who throw ridiculous amounts of money at their security. It somehow never seems to work though, some of the victims had incredibly good security, yet somehow they're dead now anyway.

Another group of Rich People start using their connections and lobbying politicians for better security for themselves, arguing that it's the state's job to keep them safe. When this becomes public, they gain a huge shitstorm. In the public's eye they've been hiding their money away for years, and now they want taxpayers' money for themselves, too.
The third group starts seriously considering giving away their wealth. Of course, in the back of their minds, the question keeps coming up - how much can I keep and still be safe? #TaxTheRich gains traction and lots of support from Group 3.
All the while, the murders continue. First, it's just one country in Central Europe. But then, the first murder occurs in a neighbouring country. Then, another. Then, yet a new one, this time in a third country.
Is this really just one serial killer? Is it, maybe, a whole movement? Last Generation spinoff? Extremist radical leftists? If they're organized, how do they communicate? Are there individual copycats, and not an organized group? Maybe loosely associated, like Anonymous?
And how do they keep succeeding, how in the hells are they getting the intel required to pull off their hits? Who are their informants, how do they even determine who's "worthy" of their attention? Surely it's not the #DeathTo Hashtag that's popped up on social media, is it?

Here and there, a suspect is caught. Some are believed to have committed a murder, some seem innocent. But the murders continue. And they're starting to spread. At first it was just Europe, but now the first cases pop up in the US.

But hey Dirk, I hear you say, a few paragraphs up you were talking about four groups of Rich People, but you ever only mentioned three of them.

That's true, but I wanted to let the murder spree spread to the US first. Now, the fourth group of Rich People is a very small group of deranged millionaires. Imagine someone, I don't know, maybe running for a high, prestigous, political office.
They're posting in all caps on their personal social medium, complaining about how despite being so very rich, there's never been an attempt on their life! (Please keep in mind this is an idea of fictional content).