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Hello
I got the following questions from one book of grammar.

Decide whether the following relative clauses are defining or non-defining:
4. My students who asked for extra work have been doing very well on the exams. (in this sentence, all of "my students" asked for extra work)

5. My students who asked for extra work have been doing very well on the exams. (in this sentence, only a portion of "my student" asked for extra work and they are the ones who have been doing well).
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question 5 it is clear defining relative clause and no comma is needed = particular students ( not all the students) but all those who who asked for extra work have been doing very well on the exams (Perhaps or surely there are other students who did not ask for extra work and it maybe they did not share the exam as well ) Clearly defining relative clause

The problem is with sentence 4 : If consider it defining then it goes incorrect according to the information given.
And it is the same way if we put commas around the adjective clause
I think or let say I am sure the sentence is wrong patterned
Therefore, I suggest editing it as the follow :

My students, who have been doing very well on the exams, asked for extra work. (in this sentence, all of "my students" asked for extra work)
In this it goes right with the information given ( We can leave the extra information and the sentence will not lose meaning)

My students asked for extra work. = all the students

Is not here a native teacher or someone is excellent in grammar to see whether he or she agrees with me or not.

Questions are from the book : A New Form-Function Grammar of English - Page 273

EXERCISES
A. The following sentences are written completely without punctuation. Rewrite each of the sentences, identifying the relative clause in each sentence. Be sure that your punctuation indicates whether the relative clause is a restrictive or non-restrictive clause.
Examples: The sign that they tore down had valuable information —) The sign that they tore down had valuable information.
"that they tore down" is a restrictive relative clause and commas are not necessary to separate it from the main clause.
The President and his family reside at the White House which stands at 1600 Pennsylvania Ave. in Washington DC 4
The President and his family reside at the White House, which stands at 1600 Pennsylvania Ave. in Washington DC.

footnote: Which could formerly be used for human antecedents, as in certain versions of the Lord's Prayer. Our father which an in heaven....

You are right. In any case, 4 and 5 are written identically so they cannot both be defining or non-defining.

Btw, “on the exams” is not idiomatic. It would normally be “in the exams”, at least in British English and I’m pretty sure in American English too.