Disclaimer: I am not a psychologist nor am I trained in psychology.
Preface: I write this not necessarily for the benefit of the student described in the question, but for a general audience of academics and students, who may encounter such social situations in the course of their studies or careers, in the hopes that it may lead to an improved understanding and ability to prevent such problems from escalating.
Many students, at some point in their academic careers, engage in avoidant behavior in response to academic stress. This of course is not productive in the long term, but in the short term, it provides some measure of relief from what they feel is an overwhelming burden they perceive they cannot overcome no matter the amount of effort spent. This eventually can lead to fatalistic attitudes toward academics and the self-fulfillment of failure.
This type of response, avoidance coping, is also associated with depression, low self-esteem, and impostor syndrome, both as causes and as effect; however, addressing such a relationship is not in the scope of this discussion. More importantly for the advisor to understand is that avoidance coping frequently occurs on a spectrum of degrees and not only at the extreme: students may continue to make some effort, such as seeking help from peers, but a sense of embarrassment or shame over struggling or feeling as if they have let their advisors and mentors down, may be precisely the reason why they do not seek help from those who are objectively the most qualified and able to provide it. Advisors are often perplexed by what they observe as sudden loss of communication ("ghosting" in the parlance of the day), and may attempt to compensate by what they believe is the most logical response, which is to confront the student and try to reopen a dialogue. However, once this pattern of avoidance emerges, such efforts can actually be counterproductive, because it not only serves as a reminder of the stressors the student is trying to avoid, but it now compounds the stress because the student is interpreting the advisor's inquiry as a demand for contact, rather than an offer for help. As a result, the student merely digs in further, feeling as if they have doubly failed--academically and interpersonally.
With this context in mind, sometimes it is not possible for advisors or mentors to "rescue" the student, especially if this avoidance behavior builds up prior to an important milestone, such as a thesis defense. In my experience, what seems to work best is showing that the student's perceptions of futility and incompetence are distorted, and that success remains within reach--if accommodations can be made to make it so. Relieving the perceived burden, breaking it down into smaller, more manageable tasks, and reinforcing positive, approaching behaviors through rewards and encouragement, is necessary in order to build a student's self-confidence.
So, what does an advisor or mentor do? First, I believe it is crucial to identify early signs of avoidance coping before it becomes entrenched, and to keep students motivated by reminding them that they are making progress. If the coursework or research is too copious or difficult, help them break it down into smaller problems. Explain to them that this is an essential life skill to learn, more so than the actual work itself.
If, however, a student has already "ghosted" you, then you need to step back a bit in your role as advisor. Rather than trying to remind them of their academic duties, you might ask them to come see you during office hours, and have a face-to-face interaction in which you would ask about how they feel about their academic situation. If they acknowledge being overwhelmed, suggest they look into student counseling. If you are able, offer to postpone upcoming due dates or modify the structure of their curriculum or research, or terms of their academic progress, but only conditional upon their agreement to recommit themselves. They need to be able to speak to someone with the power to make such adjustments. If the institution is not willing or able to do so, then the intervention was already too late.
Again, not all students behave this way, and not all students who do behave this way are doing so for the reasons I described. And not all students can be "rescued," nor is it anyone's obligation to do so. But for some, it is absolutely worthwhile, because they can and do respond remarkably well once they are given the right framework to learn how to apply positive coping mechanisms. Some students never learned how to cope with overwhelming pressure, and if they are not taught, they merely grow up into adults who still do not know how, and in my mind, that is far worse an outcome than not completing a degree.