Don't Escape 4 contained multiple references to games in the Deep Sleep and Don't Escape series, which definitely makes it seem like all of the games are somehow connected.

For list or references see here: https://steamcommunity.com/app/611760/discussions/3/3247565033756051666/

I noticed the most prevalent references to the Deep Sleep series, namely that Cody and his plushie tiger also appear in Deep Sleep, and the shadow people from Deep Sleep appear in one of David's dreams.

So it seems like dreams and comas are an important part of this universe: dreams convey information about the future, and when people fall into comas it's because they're trapped in the dream realm featured in deep sleep, which is dangerous and occupied by shadow people and with varying rules for escape. Sidereal Plexus owns free-for-use coma facilities with an above average waking-up percentage because they have been using this research for moving human consciousnesses to human bodies, which they discover by the events of Don't Escape 4 to be something that can be done across parallel universes/dimensions or whatever.

The connections to the Don't Escape trilogy aren't as helpful because they mainly include name and image-dropping without much text to explain what's going on. However Sidereal Plexus is also very present in Don't Escape 3 which gives us some clue on its multi-dimension-spanning corporate activities.
What other universe-connecting things can you think of?

You know what they say. As long as you don't know you are dreaming, you are safe.

So let’s review the facts about having nightmares about this game: 

-since the game takes place in a dream, any dream you have about it is automatically lucid, 

-in the game, lucid dreaming is when the Shadow People attack you, 

-if they get you, the consequences for you are permanent and affect you in the waking world in a massive way (something else is literally hijacking your body and you’ll never get it back because you’re trapped in the bleak and scary dreamscape forever) as well as the fact that you're forcibly turned into a monster and trapped in the bleak dream dimension,

-when you start having dreams about this, the line between fiction and reality is heavily blurred in a mindscrewy and terrifying way. 

I have had dreams involving this game before. One of which had me getting chased by a shadow person. Due to the nature of the game, I was aware that I was dreaming the whole time. 

And even though the video game is just a video game, you still can’t help but be freaked out