I was snacking on my new fave low-carb treat, Crystal Light popsicles, when I had a thought. Why can’t I make these myself?
But one of the best parts is the texture, slightly crunchy and easily yeilding to the teeth. If I poured some Crystal Light into a popsicle mold it would come out hard as a rock?
How do they do it?
I think it is because they are made by freezing a solution of water, sugar, and other things. As this freezes, the mix ratio in what freezes is different from the remaining liquid, and the areas that freeze last have a pretty different mix ratio (and freezing temperature and hardness) than the areas that freeze first.
Cecil discusses the term “quiescently frozen”, but doesn’t discuss the resulting consistency.
At HowStuffWorks, they say stabilizers are added.
I propose an experiment. Allow a Crystal Light popsicle to melt, and refreeze it in an ice cube tray. Also try freezing some Crystal Light at the same time (maybe at a couple different concentrations), and see if they are different.
ETA: Even easier: Read the ingredient lists on the two products, and see what’s different. Google or someone here would probably know what the extra ingredients do.
A large factor is how fast they freeze them. Freeing fast allows two things to happen (or not happen, as the case may be)
The ice crystals that form don’t get a chance to “merge” and become really large before everything is frozen.
The solution doesn’t have a chance to separate before it’s frozen, which would result in the bottom being sugary, sweet, and barely frozen while the top is rock hard, as sometimes happens with homemade popsicles.
The board search this morning doesn’t like me, but there was a thread in CS not too long ago about what to add to juice for good home-made popsicle mix. Gelatin products or pectin both came up, IIRC, as something that would resist ice crystal formation partially and thus help the ‘crunch factor’
Actually, I was one of the people who mentioned gelatin - specifically, an old recipe for popsicle mix with jell-o and kool-aid in it. 
Finally on preview: aha, here the thread is! The secret to homemade popsicles...why so watery? - Cafe Society - Straight Dope Message Board
I once tried freezing Jello-O, which came out to a remarkably popsicle-like texture so here’s another mention of using gelatin. You can buy it unflavored (Knox is a common brand), add it to your favorite juice (like Crystal Light) and freeze it yourself.
This was the first thing that occurred to me, but nothing I found online ever mentioned it.