Purification in Delos

I was just reading in "T-Diddy" (our good friend Thucydides, Book 3.104 if you want to know) how the Athenians purified Delos.

"All the remains of those that died in Delos were removed, and for the future it was commanded that no one should be allowed either to die or to give birth to a child in the island; but that they should be carried over to Rhenea" which is near to Delos.

What I'm really concerned about is that part about people not being allowed to die or give birth on the island. This raises a few questions in my mind, and I'm sure it does the same in yours. The birthing part is pretty simple, it's weird but it's simple. They just put all their maternity wards on this island of Rhenea, problem solved. Also, people generally know when they're going to have a baby. There's a few signs to look out for (but keep your guesses to yourself). So, when those signs present themselves they send them over to that other island. But what if the signs were just missed? This happens you know.

Delos Purification Authority: Excuse me maam, you aren't about to have a baby here are you?

Woman in labor: I know, I know I saw the leaflets; I'm not supposed to give birth here. But I didn't know I was, and now I am.

DPA: I'm sorry maa'm but you are going to have to go to Rhenea for that. I can't allow you to have a baby here.

Dang, shucks for her. What a hassle.

And what about people dying? There had to have been more cases of ambiguity then. I mean, after a certain age I guess they just ferried the old people to Rhenea, and the same with the sick. I'm guessing there were no beds designated as "death beds" in Delos. But what about the odd person who started dying unexpectedly.

DPA: Um. . . Sir, you look like you could die any minute now. When did this start?

Dying man: About. . . ten minutes ago. . . I can hardly breathe.

DPA: Well dying's not allowed here, you're going to have to go to Rhenea. I shouldn't have to tell you this.

DM: Rhenea? I heard it's terrible, I want to die here.

DPA: Too bad, that's the law.