In the Buddhist tradition, there is no birth and no death, only a continuous change in form. This is described in the following passage from Thich Nhat Hahn’s book No Death, No Fear: Comforting Wisdom for Life (Riverhead Books, 2002, pages 25-28):

Sometimes people ask you: “When is your birthday?” But you might ask yourself a more interesting question: “Before that day which is called my birthday, where was I?”

Ask a cloud: “What is your date of birth? Before you were born, where were you?”

If you ask the cloud, “How old are you? Can you give me your date of birth?” you can listen deeply and you may hear a reply. You can imagine the cloud being born. Before being born it was the water on the ocean’s surface. Or it was on the river and then it became vapor. It was also the sun because the sun makes the vapor. The wind is there, too, helping the water to become a cloud. The cloud does not come from nothing; there has only been a change of form. It is not a birth of something out of nothing. 

Sooner or later the cloud will change to rain or snow or ice. If you look deeply into the rain, you can see that the rain is transformed into grass and the grass into cows and then to milk and into the ice cream that you eat. Today if you eat an ice cream, give yourself time to look at the ice cream and say: “Hello, Cloud, I recognize you.” By doing that you have insight and understanding into the real nature of the ice cream and the cloud. You can also see the ocean, the river, the heat, the sun, the grass and the cow in the ice cream. 

Looking deeply, you do not see a real date of birth and you do not see a real date of death for the cloud. All that happens is that the cloud transforms into rain or snow. There is no real death because there is always a continuation. A cloud continues the ocean, the river and the heat of the sun, and the rain continues the cloud.

Before it was born, the cloud was already there, so today, when you drink a glass of milk or a cup of tea or eat an ice cream, please follow your breathing. Look into the tea or the ice cream and say hello to the cloud.

…If we are afraid of death it is because we have not understood that things do not really die….I have a photograph of myself when I was a boy of sixteen. Is it a photograph of me? I am not really sure. Who is this boy in the photograph? Is it the same person as me or is it another person? Look deeply before you reply.

There are many people who say that the boy in the photograph and I are the same. If that boy is the same as I am, why does he look so different? Is that boy still alive or has he died? He is not the same as I am and he is also not different. Some people look at the photograph and think the young boy there is no longer around. 

A person is made of body, feelings, perspectives, mental formations and consciousness, and all of these have changed in me since that photograph was taken. The body of the boy in the photograph is not the same as my body, now that I am in my seventies. The feelings are different, and the perceptions are very different. It is just as if I am a completely different person from that boy, but if the boy in the photograph did not exist, then I would not exist either. I am a continuation, like the rain is the continuation of the cloud.