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This will probably be my last question regarding my prior questions. This will
particularly focus on `adjective + 物/こと`. I was finally able to minimize the
mess in my head, narrowing it down into something simple but I lacked of. I
only learned about relative clause by verbs which sudden appearances of
relative clause by adjective seems confusing.

I know that 見た犬 can either mean "the dog that saw" or "the dog (I/he/you) saw"
depending on the context. Does that mean relative clause of adjective also
have 2 possible meanings?

In this example:

> 私が好きな猫

It can mean "the cat I like" or "the cat that likes me". I don't know how it
can be like that (especially that like is an adjective), how can it be? 白い物
means the thing that is white, can it have another meaning? 白いこと means being
white, can it have another meaning?

For verbs the relative clause can be the subject or object (except if it is
non living things and if the context is clear). Please explain it to me
regarding this as detail as possible. Thank you for helping!
教えてください。すみません！ありがとうね。
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relative-clauses nominalization
How do adjectives work in relative clauses?
You understand right that relative clause of adjective can also have 2
possible meanings. For example, 「好きな人」 may not only mean "the man/woman" who
(I) love", but also "the man/woman who likes something" whenever it's implied
by the context (compare 「私の好きな人」 and 「寿司が好きな人」).

Grammatically you can also say 「寿司が白い人」 (a such man that sushi are white for
him), but this phrase lacks a common sense for me. You can try with other ～い
adjective, though.
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This phrase "見た犬" is ambiguous. 私が見た犬 means "the dog I saw" and 私を見た犬 means
"the dog that saw me".

In the case of 好きな猫 is same. 私が好きな猫 means "the cat I like" and 私を好きな猫 means
"the cat that like me".

白い物(こと) means only "the thing that is white".
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**I think the comparison of 好きな to 白い is not a fair comparison, which results
in strange interpretations of the sentence if you enforce the situation that
is true for one word, onto the other word.** Let me try to explain.

好き is not a normal な-adjective, it does not behave in the same way as other
typical な-adjectives. Kuno calls it a Verbal Nominal Adjective. Verbs take を
for object marking while a **Verbal Nominal Adjective such as 好き takes が for
object marking**.1 Now let's try to label the different が.

I will label them such that が1 is our usual subject marker, while が2 is the が
that is used when 好き is around to assign the が2 argument marker.

Now let's first look at the structure. We begin with a usual verb like 読む and
then swap it out with 好き:

>   1. 私が１ 本を読んだ = "I read a book"
>
> We can choose 本 or 私 as our noun of interest and proceed to make relative
> clauses:
>
>     * **[A]** Choosing 本: (私が１読んだ)P本 = "The book that I read"  
>  Notice that the **object marker を is not present** in the relative clause
> P.
>     * **[B]** Choosing 私: (本を読んだ)Q 私 = "I (that read the book)"  
>  Notice that the subject marker が1 is no longer present.
>   2. 私が１ 猫が2好きだ = "I like cats"
>
> We can choose 猫 or 私 as our noun of interest and proceed to make relative
> clauses:
>
>     * **[C]** Choosing 猫: (私が１好きな)R猫 = "The cat that I like"  
>  Similarly notice that the **object marker が 2 is not present** in the
> relative clause R.
>     * **[D]** Choosing 私: (猫が2好きな)S私 = "I (that like cats)"  
>  Notice that the subject marker が1 is no longer present.
>

Now a slightly different case where we interchange 私 and 猫. We do the same
thing of using a usual verb 読む and then swapping it out with 好き:

>   3. 猫が１(本を読んだ) = "The cat read a book"
>
>     * **[E]** (本を読んだ)X猫 = "The cat that read a book"  
>  This is analogous to **[B]**.
>   4. 猫が１ (私が2 好きだ) = "The cat likes me"
>
>     * **[F]** (私が2 好きな)Y猫 = "The cat that likes me"  
>  This is analogous to **[D]**
>

Now we put **[C]** and **[F]** side by side and remove all the labels. Both of
them are on the surface:

>   5. 私が好きな猫 with two possible ways to label them:
>
>     * **[C]** (私が１好きな)R猫 = "The cat that I like"
>
>     * **[F]** (私が2 好きな)Y猫 = "The cat that likes me"
>
>

* * *

Next let's go back to what I was trying to explain in the first sentence in
this answer, why it is not fair to compare 好き to 白い:

  * 白い does not assign an argument for an object.

  * Now we shall try against all rules to form an analog of Sentence 1. or 2. above such that 物 replaces 私

    * 物が1+[？を]+白い
    * 物が1+[？が2]+白い

We soon realise that it cannot be done because 白い has no argument for an
object and the sentence 物が1白い is already complete.

Consequently there is no choice as in sentences 1. or 2. for you to choose
your noun of interest and you are left with (in analog to the above examples):

>   * **[G]** Choosing 物: (白い)物 = "Thing that is white" = "white thing"
>

So to answer your question if there are additional meanings to 白い物 since
私が好きな猫 gave you reason to suspect that there might be other interpretations,
**there are no other interpretations for 白い物 in the way that 私が好きな猫 has.**

* * *

References:

[1] _The Structure of the Japanese Language_ , p.90-91, Susumu Kuno
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