The sentences you created do not represent equivalent transformations. It's more like this:
- Definite: "The good idea of Tom's" and "Tom's good idea"
- Indefinite: "A good idea of Tom's" and "One of Tom's good ideas"
The possessive determiner is definite. In the last phrase, "One of Tom's good ideas", it is speaking of the definite set "Tom's good ideas", but is selecting one indefinite idea from the set.
Your question is really about English determiners. Determiners can express the noun's reference in many ways, including definite, indefinite, quantity, possessive, etc. A list of English determiners is given here: http://en.wiktionary.org/wiki/Category:English_determiners
There are several theories of determiners, and it is an area of linguistic study. There are also many variations and special cases, so there's no single rule that covers all situations. One aspect is based on familiarity of the NP to both the speaker and the listener. A related aspect is whether the information is new/unknown/not-yet-introduced or old/known/introduced previously.
In the Noun Phrase (NP) "A good idea of Tom's", the "good idea" is one (indefinite) "idea" of possibly many. For example,
- A good idea of Tom's is to build a bridge. The idea is known by the speaker, but the speaker assumes the listener does not know which one he is referring to until after he explains it.
Sometimes the indefinite article is used to introduce an NP and the definite article is used after that. This can be based on the new/old unknown/known aspect of determiner theory:
- A good idea of Tom's is to build a bridge. The idea is that if we build a bridge, we can eliminate the ferry and traffic congestion. In the first sentence, the idea is introduced. In the second sentence it should be clear to the listener (reader) to understand which idea is being referred to.
The following NP uses the possessive determiner:
The dog is first being qualified as the one and single "good dog" that is owned by John. As such, this determiner is "definite". In context, the word "good" might also be acting as a determiner. The speaker could be indicating Tom's one particular good dog rather any of his other bad dogs. Otherwise, "good" is simply being descriptive of his dog.
The following is similarly possessive (and determinate):
Here the speaker is referring to a particular good idea that Tom has. It is similar to this:
Finally, note that your phrase "A good idea of Tom's" could be rephrased as "One of Tom's good ideas"
Note that in google search, "unknown noun phrase" does not have many results, so that's not a common terminology in English.