Assuming that you refer to your recent related question, I'll elaborate some more on Greg Lee's answer (which I think already brings the main issue of the problem quite well to the point), hoping that this should clarify your question:
The so-called Ross Constraints ("Constrains on reordering transformations") are a set of constraints from around 1967 trying to capture which syntactic transformations are allowed within sentences and which not. To mention the most relevant ones:
The complex NP constraint (CNPC)
No element contained in a sentence dominated by a noun phrase with a lexical head noun may be moved out of that noun phrase by a transformation.
This basically means that you can't relativise an NP (noun phrase) that is itself a relativisation of an NP.
Example:
1) a. [the man] who I saw [] yesterday
b. * [the man] who I believe [the rumours that [] is a murderer]
1a. is grammatical, but 1b. isn't, because the man was moved out of another noun phrase (the rumours ...) which is not permissible in English.
The coordinate structure constraint (CSC)
In a coordinate structure, no conjunct may be moved nor may any element contained in a conjunct be moved out of that conjunct.
"Coordinate structures" are constructions where several constituents are conjoined by words like and, or, etc.
Example:
2) a. [the tree house] that [Mary had built [] for her son and her daugther]
b. [her daughter] that [Mary had built a tree house for [] ]
c. * [her daugther] that [Mary had built a tree house for [her son and [] ]]
2a-b. are okay, but 2c. isn't because the NP her daugther was moved out a coordination between to NPs (her son and her daughter).
The sentential subject constraint (SSC)
No element dominated by an S node may be moved out of that S if that node S is dominated by an NP which itself is immediately dominated by an S.
This sounds a bit complicated, but is actually quite straightforward.
3) a. [the neighbour] who [that John played loud music] bothered []
b. * [the music] which [that John played loud []] bothered the neighbour
3a. is okay (though weird to say, but I don't think its ungrammatical), while 3b. is not: The NP the music has been moved out of the play-sentence ("an S-node") which is the sentential subject (XY bothered the neighbour) of the bother-sentence ("an NP which is itself immediately dominated by an S"), which is not allowed.
As usual, even for English there are restrictions to the applicability of such constraints:
4) a. * [Ms. Smith], [that [] lost her son]] is a tragedy
b. [Ms. Smith], [that [she] lost her son]] is a tragedy
While 4a. is ungrammatical according to the SSC (Ms. Smith has been moved out of the lost-sentence which is the sentential subject of the tragedy-sentence), 4b. is not due to the so-called resumptive pronoun (she), a pronoun which was left in place when dislocating Ms. Smith to the left side of the sentence.
This is where the terminology that Greg Lee also mentioned, "copying transormations" (where a "copy" in shape of a resumptive pronoun is left) vs. "chopping transformations" (where the NP is simply "cut out" of the sentence), comes into play.
These constraints were supposed to be universals, but in fact are not: According to my understanding, the sentences 1) and 3) (I don't know about 2)) are, though not in English, allowed in Japanese.
There are a lot more problems to these constraints and over the years the formulations have been heavily revised (after all the constraints in their original are half a century old), but for the sake of your question as far as the differences between English and Japanese are concerned, one could narrow it down to saying that these are the cases where relativisation is not permitted, while in most other environments it is.
To come back to your question: No, your predictions are not correct.
5) a. [[The dog]ᵢ [that the boy loved []ᵢ ]] died
b. This is [[the dog]ᵢ [that the boy loved []ᵢ ]]
In both cases (the dog as a subject or as an object to the sentence) there is no problem with relativising the dog, and there is no problem either with further attaching relative clauses inside the relativisation:
6) a. [[The dog]ᵢ [that the boy [that lives next to my house] loved []ᵢ ]] died
b. This is [[the dog]ᵢ [that the boy [that lives next to my house] loved []ᵢ ]]
Relativisaiton in the sense of recursively embedding relative clauses in another relative clause is not restricted in any way, you could do this forever:
c. [[The dog]ᵢ [that the boy [that lives next to my house [that I've inherited from my father [who I admired]]] loved []ᵢ ]] died
What is, however, not permitted, is moving these elements out of their relative clauses and make them the main relativised element (the head of the complex construction) themselves:
7) a. * [They boy]ⱼ that [[the dog]ᵢ [that []ⱼ ... loved []ᵢ] died]
b. * This is [my house]ⱼ [that [[the dog]ᵢ [that the boy [that lives next to []ⱼ ] loved []ᵢ ] died]
The problematic elements ([the boy]ⱼ/[my house]ⱼ) are moved to the front by relativisation, leaving a gap ([]ⱼ) that is embedded in a construction that already relativised another element ([the dog]ᵢ), which is not allowed.
If I understood the cited passage in your other quesiton correctly, this is what makes the difference to Japanese.
Two wrap up the main point of my answer again:
As I understand it (and as I suppose Greg Lee understood it), the wording in the paragraph you cited is imprecise and probably be the source of the problem. NPs within RCs can be relativized, in fact infinetlely so, as demonstrated by sentences 6). The only thing that is not possible is movement of the embedded relativized element to the beginning of the sentence to make them the head of the whole construction, as shown in sentences 7).
That "NPs within RCs can't be relativized" is not true, and not what the paragraph wanted to say. What the paragraph wanted to say instead (and expressed very ambiguously, I admit), is that movement of the embedded relativized constituents to the front of the sentence is not possible under some conditions, namely the ones described by the mentioned constraints.
My answer is that I think the issue results from a misinterpretation of an ambiguously written statement, and that what the paragraph actually was meant to say is what I described with the constraints (which are the answer to the question "Which NPs within RCs can be relativized").
