What do I do when a student working in my lab "ghosts" me?

I wrote him mails on a weekly basis asking for a status update and inquiring whether he was stuck.

It seems that you are completing your duties as an advisor well. You can and should continue to offer help and suggestions in accordance with your duties. Perhaps this student is too busy or too anxious to respond to your emails. In that case, you could provide links to resources that might benefit them without the necessity of responding (if you feel that they need more advising).

While I personally try to respond to emails in a timely fashion, I often work better independently and only reach out when I am in need of assistance; this student might function the same way.

I already have escalated the issue to my supervisor

Great, this means that your supervisor is aware of the issue and is likely to be understanding in the event that your student does not do well.

he told me to let it student fail if required

This is also fine. If the student does not adequately complete their work, this is the expected outcome. If you are concerned that the student is unaware of this, you could send an email letting them know (or possibly reminding them of policies in the syllabus regarding this).

Are there other options for me?

You cannot force the student to respond or work on their project. You should continue to advise this student to the best of your ability, but beyond that it is their responsibility to follow through.

Your supervisor is correct. Let the student fail.

I'm shocked the existing answers are so lenient. You have given the student an amazing opportunity to work with your group, and from the tone of your question, I assume you have been providing adequate guidance and support. In response, the student has "ghosted" you. This is unacceptable.

If you have not already done so, I would send a much more blunt message to the student. "Regular check-ins with me are required for all undergraduates in the lab. Please schedule an appointment for within the next week. If I do not hear from you, I will assume you are not interested in continuing with your thesis."

After that, the ball is in the student's court:

• If they do make an appointment, I would have a discussion about what happened. Based on the student's tone in this discussion, I would decide whether to proceed (in consultation with the advisor, in your case).
• Otherwise, no further action is needed from you. Either they'll show up with a completed thesis -- which your advisor will have to deal with -- or they'll never be heard from again.

An alternate approach, not of the "sink or swim" school, is to see what office in your university provides student services. In the US, a college or university will normally have a Dean of Students, part of whose job is to look after student interests and well-being.

There may or may not be anything they can do, but if you have any suspicion that the student is suffering from depression, you can contact them. They may be limited in their ability to approach a student, but it might be worth talking to that office.

There is, by the way, the concept of self-defeating behavior and even self-defeating personality behavior that might require professional assistance.

You and your department head or supervisor are not the right people to deal with such situations, of course.