Should someone continue with their PhD if they fail the core courses in master's?
I'm going to answer here as if you are the &quot;friend.&quot;
If the university accepts you into a doctoral program they have fairly high confidence that you will be successful. Otherwise they are just wasting scarce resources, including money, space, and faculty time.
It may be that you have some deficiencies and I hope that the educational system in place gives you the time and opportunity to fill any gaps, but you probably also have some compensating points in your favor.
It is good, of course, to try to figure out why you had issues in the past and to correct what can be changed.
But doctoral work is different from coursework and the skills required are not the same. Trust the people who admitted you to the program that you can do it.