The thing with serial killing, is that it is very difficult to hide.
Some of the hardest cases can be for instance a nurse at a hospital killing in a way that appear natural.
But even that gets detected quicker than you would think, because while 1 killing can be a fluke death, already at 2 killings, it can throw off the statistics and cause an investigation. With 3 it’s almost impossible the incidents can’t be tracked back to the person who did it.
An other situation can be a woman who kill their husband for inheritance, and then does it a second time. That second time is usually enough for alarm bells to sound for families of the deceased. Resulting in more thorough police investigations.
Obviously it can happen they get away with it, but I’m confident, that by far the most serial killers are caught, because it’s insanely difficult to hide multiple killings.