It is said in the Bhagavad gita 2.22:
http://www.vedabase.com/en/bg/2/22

"As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones."

Pay attention to "giving up the old and useless ones".
So the Gita says that this is why the soul must leave the body, ie when the body becomes useless because of bodily damage or old age.
Of course all this happens because of karma of the soul.

The soul is attached to the body! It is not true that he is not attached to the body!

Update:

Jatin, that what you have said in your edited post "Therefore it is soul that should initiate the process of death" simply is not true! The soul does not initiate anything, for he is just a passive inhabitant of the body in this case. The soul is forced to leave the body in a certain moment because of his own karma, and this is called death.
Now, the question is why the soul at a given moment must leave the body? This is due to karma, or predestination. About that you can read in my two questions here:

Is the length of a man's life predetermined?

Can it happen that the length of a man's life somehow becomes reduced during a man's lifetime, and so one has to die before he was destined initially?

It is said in the Bhagavad gita 2.22:
http://www.vedabase.com/en/bg/2/22

"As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones."

Pay attention to "giving up the old and useless ones".
So the Gita says that this is why the soul must leave the body, ie when the body becomes useless because of bodily damage or old age.
Of course all this happens because of karma of the soul.

The soul is attached to the body! It is not true that he is not attached to the body!

Update:

Jatin, that what you have said in your edited post "Therefore it is soul that should initiate the process of death" simply is not true! The soul does not initiate anything, for he is just a passive inhabitant of the body in this case. The soul is forced to leave the body in a certain moment because of his own karma, and this is called death.
Now, the question is why the soul at a given moment must leave the body? This is due to karma, or predestination. About that you can read in my two questions here:

Is the length of a man's life predetermined?

Can it happen that the length of a man's life somehow becomes reduced during a man's lifetime, and so one has to die before he was destined initially?

It is said in the Bhagavad gita 2.22:
http://www.vedabase.com/en/bg/2/22

"As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones."

Pay attention to "giving up the old and useless ones".
So the Gita says that this is why the soul must leave the body, ie when the body becomes useless because of bodily damage or old age.
Of course all this happens because of karma of the soul.

The soul is attached to the body! It is not true that he is not attached to the body!

It is said in the Bhagavad gita 2.22:
http://www.vedabase.com/en/bg/2/22

"As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones."

Pay attention to "giving up the old and useless ones".
So the Gita says that this is why the soul must leave the body, ie when the body becomes useless because of bodily damage or old age.
Of course all this happens because of karma of the soul.

The soul is attached to the body! It is not true that he is not attached to the body!

Update:

Jatin, that what you have said in your edited post "Therefore it is soul that should initiate the process of death" simply is not true! The soul does not initiate anything, for he is just a passive inhabitant of the body in this case. The soul is forced to leave the body in a certain moment because of his own karma, and this is called death.
Now, the question is why the soul at a given moment must leave the body? This is due to karma, or predestination. About that you can read in my two questions here:

Is the length of a man's life predetermined?

Can it happen that the length of a man's life somehow becomes reduced during a man's lifetime, and so one has to die before he was destined initially?