No. LLMs do not have memory like that (yet).

Your 'scary' examples are very hypothetical and would require intentional design to achieve today; they would not happen by accident.

Chapter 4: In Which Phileas Fogg Astounds Passepartout, His Servant

Just as the train was whirling through Sydenham, Passepartout suddenly uttered a cry of despair.

"What's the matter?" asked Mr. Fogg.

"Alas! In my hurry—I—I forgot—"

"What?"

"To turn off the gas in my room!"

"Very well, young man," returned Mr. Fogg, coolly; "it will burn—at your expense."

- Around The World in 80 Days by Jules Verne, who knew that leaving the heat on while you went on vacation wouldn't burn down your house, 1872.

When you think about the damage that could be done with this kind of technology it’s incredible.

Imagine asking your MixAIr to sort out some fresh dough in a bole and then leaving your house for a while. It might begin to spin uncontrollably fast and create an awful lot of hyperbole-y activity.

All of those outcomes are already accessible by fat fingering the existing UI. Oven won’t burn your house down, most modern ones will turn off after some preset time, but otherwise you’re just going to overpay for electricity or need to replace the heating element. Unless you have a 5 ton industrial robot connected to your smart home, or have an iron sitting on a pile of clothes plugged in to a smart socket, you’re probably safe.

If it wasn't dangerous enough by default, he specifically instructs it to act as much like a homocidal AI from fiction as possible, and then hooks it up to control his house.

I think there's definitely room for this sort of thing to go badly wrong.