Judaism teaches that all human life is sacred. People were G-d’s special creation, and each individual is known by G-d, who plans their lives and decides how long they should live.
Your eyes saw my unformed limbs;
they were all recorded in Your book;
in due time they were formed,
to the very last one of them (Psalm 139:16).
The Torah was given to humans ‘so that they might live’. Suicide is a sin. ‘One who intentionally takes one’s life has no share in the world to come.’
So Judaism cannot approve of euthanasia because only G-d can decide when a person should die.
The teaching of Rabbi Moses Isserles is sometimes used to argue that life-support machines should be turned off if there is not hope of the patient’s recovery:
If there is anything which causes a hindrance to the departure of the soul … then it is permissible to remove it.