I could have the wrong end of the stick here, but your second example doesn't make sense to me.
Part 1: regular relative clause
Let's look at your first example first.
At its core (haha, pun not intended), we have:
I pilfered the apple.
The relative clause portion tells us more about the apple:
[(it) was on the plate]
Looking at the whole utterance, we get:
I pilfered the apple [(that) was on the plate].
Part 2: nominalized clause
Now let's look at your second example.
The core here is more complicated, because we don't have a simple concrete noun as the object of our verb くすねた. Instead, we have the の, which here is used to nominalize (make a noun out of) the entire preceding clause.
So let's look at the embedded clause.
[The apple was on the plate]
Okay, simple enough.
After this, though, we have that の, turning our entire embedded clause into a nominalized phrase. This can be a bit messy to translate into English; it comes through somewhat similar to "the fact that", or "the act of", or sometimes by turning a verb into the "-ing" form. Some examples:
I like (the act of) eating ramen.
Note that this is different from just "I like ramen". We're not talking about "ramen" as the main noun, but rather about the whole clause that contains "ramen" -- in this case, about "eating" it.
I didn't know (the fact) that Michiko went to Tokyo.
Again, this is different from "I didn't know Michiko". We're not talking about "Michiko" as the main noun, but rather about the whole clause that contains "Michiko" -- in this case, that she "went to Tokyo".
Looking again at the whole second example sentence then:
The key is that it turns the whole embedded clause into a kind of noun: we're not talking about "the apple" anymore, but rather the fact that "the apple was on the plate".
Because of the verb here, くすねた / "pilfered", nothing quite makes sense -- just due to the meaning of the words, this doesn't fit together. The best translation I can come up with would be something like:
I pilfered (the fact that) [the apple was on the plate].
...??? That doesn't make sense in English. Nor does the Japanese make sense. (At least, as I understand it.)
If you change the verb from くすねた to 見た, that would work:
I saw (the fact) that [the apple was on the plate].
The paper in question appears to be this one:
This seems to have been written by a native speaker of Japanese, which makes that second sample sentence a bit of a head-scratcher for me.
For the verb くすねる, I'm only aware of the sense "pilfer, filch, sneak, pinch, swipe", with the core underlying meaning of "to steal something sneakily". There might be a sense of くすねる that I'm missing, which could make the second sample sentence work better.