Relative clauses are categorized into two types in terms of restricting meaning: restrictive clauses and non-restrictive clauses.
In my view, a non-restrictive relative clause cannot be used when the word before the clause is indefinite (an, an, plural forms without "the" or "those" or "these", etc).
I think this way because an indefinite word has to be narrowed down in some way in meaning.
If not, the attribute that the clause gives is applied to all the samples.
For instance, "a lion is big and eats meat" actually means "all lions are big and eat meat."
However, I found this case here, and it contradicts my idea, and I can't explain why.
My doctor is trying a new testing method, which had a 70% success rate.
Doesn't Example 1 basically mean that all new testing methods, no matter which one, had a 70% success rate?
(Source of Example 1: https://grammar.yourdictionary.com/parts-of-speech/pronouns/relative-pronoun.html)
Let's look at other examples I made here.
My brother is looking for a room to rent, which is cheap enough for a student.
Doesn't Example 2 mean that a room to rent is always cheap enough for a student?
My brother is looking for a room to rent which is cheap enough for a student.
Example 3 is what I think works the best because it means that there are different types of rooms but he is looking for a specific type of room to rent that is cheap enough for a student.