SAYER, by Adam Bash. He apparently writes much of the show, and is the title character. In other words, he provides the voice of SAYER, the Artificial Intelligence working for Ærolith Dynamics, who explains the ground rules to the company's new laborers after they arrive on the asteroid called Typhon. Follow the link, and it will take you to a page which provides access to the first 9 episodes of the series. (And the rest of them are archived on the same site.)
I have just refreshed my memory by playing back Episode 1. Here's an excerpt from the dialogue to illustrate why I feel positive that this is the same podcast you fondly remember.
"Your new home here in Halcyon Tower has everything you could ever
desire. It is truly a marvel of both architecture and urban planning.
And I can say without question that you will die here.
"That seems to be distressing you, so perhaps I am not expressing my
meaning as clearly as I intend. I simply mean to say that it is nigh
certain that your death will occur here in Halcyon. If a place
existed where your every desire could be fulfilled, would you ever
leave that place? As a rational thinker, the answer must inevitably be
. . . No. And so it is with that logic that I can deduce that you will
never leave Halcyon. So thinking about it that way, isn't that great
"You . . . still do not seem as cheerful about this as I would expect."
So you can see that you correctly remembered that "Halcyon" is a name mentioned in the podcast, though you were wrong about it being the name of the AI or the corporation.
Note: Last night, when I first saw your question, I vaguely remembered having once listened to at least the first episode, but I couldn't remember the series title off the top of my head. I figured if some diehard fan of the podcast were out there, and saw your question, then he was welcome to any rep points he could get by answering you. But tonight, when I saw that still hadn't happened, I poked around a bit and figured out which podcast you and I both remembered listening to.