Why not?
The very first responses provided by-the-book answers. Some, in the form of the death save rules, which specify that critical hits count as double failures and, since you can automatically crit someone who is adjacent to you and unconscious, it is trivially simple--by the book--to kill an unconscious character before it can be healed.
I don't think you and I have been reading the same thread. Once answers had been provided to the OP, an essentially ethical question (should a DM try to kill characters while they're helpless) arose from them that was then debated. The Jester's entirely justifiable objections to the tone of one person's posts were because there is a huge difference between saying, "I disagree with you," and "You're wrong. Please stop saying it. You're hurting the hobby." The first can be said respectfully (whether intentional or not). The second can only be said disrespectfully (for what it's worth, though, the apology that arose from that side-conversation was, indeed, respectful).
Houserules are part of the game--have been for decades. But never mind the nature of the rules, for the moment. Let's talk about the nature of a discussion. Sometimes, if someone has something to say that they think is related to the topic at hand, they will want to share it. Even if it doesn't directly answer an initial question. Especially if that question has already been answered. The discussion then takes a new course, but is enriched by the extra input. So, yeah, people are going to speak to be heard. Or is that against the rules?
Nope. The rules of D&D (and 5e, specifically) are EXPLICITLY guidelines. This means that every single DM who changes, ignores, or introduces a rule is doing it right. And so are the ones who don't.
Not sure if you're talking about shadows or wraiths, here, but, in either case they can travel through walls/ceilings/floors (in the case of the shadow, through cracks) and come back for surprise strikes later. So that hasn't really changed. Actually, with the fluidity and flexibility of 5e movement, it might even be better.