It sounds like this person is going through a tough time.
Life has easy and difficult times, sometimes very difficult times. It is good to have faith that there is light at the end of the tunnel and to contemplate on the verses of the Qur'an about Allah's mercy. Nothing stays the same forever and things often change in ways we could never imagine. Until then, however, it is sometimes necessary to walk in the darkness until reaching the light. The good thing about darkness, however, is sometimes it makes the light clearer.
Existence is not a choice, since a person who dies continues to exist. However, it is good to have faith that Allah has a plan and does not create anything in vain; just because we do not understand why we, individually, were created does not mean that we do not have our own specific reason for being.
Some might argue that Qur'an 7:172 which speaks of human beings testifying to the existence and lordship of Allah (in the realm of pre-existence, or in some other way) implies that we gave a sort of agreement to existing, even if we do not remember it now. Some might also argue that Qur'an 33:72 implies a sort of willingness to exist and accept the risks/consequences of free will, even if we currently do not want it - God knows best.
If this person is also dealing with depression or a psychological condition (either as a condition by itself or as a response to challenging circumstances), they could also look into psychological/psychiatric interventions and see if they are useful and appropriate at the moment to help get more zest for life.
If it is more of a spiritual or existential crisis (and all of the above can go hand in hand), more study and reflection of the Qur'an and theology and the big questions of life may help. In the end, while Muslims, like others, offer answers to questions such as "why do we exist?", it is one of those big questions that people have pondered for millenia, and although religions can provide answers, I think it is also something people often need to find answers for inside themselves.