In the community at large, there is a fear and suspicion of death. So far as we can tell from natural things, once a person dies, that person's thoughts and identity no longer exist. However, various religions offer the idea that the identity of a person lives on in some form.
Some believe in reincarnation, where people are born again as a different being. Depending on the religion, this may mean being reincarnated into a different type of being, such as animals, or as another human. In most cases it is not believed that the past life is remembered after ther reincarnation.
Then there is the idea that they move to some other world. This is prominent in ancient religions, such as the Egyptians. There people believed there was some form of afterlife. Many christian churches teach a similar idea with ideas such the immortal souls doctrine. In that case, the essence of a person would travel to heaven or hell on death.
In a more natural sense, people can be thought to live on through the memory of their acts, or through offspring. In some sense, the presence of a name in a history book makes that person immortalised. There are elements of this seen in the Bible, as one of the great promises to Abraham in the book of Genesis was that his offspring would become great. However, this form of continued existence is very limited in its effect, and doesn't include the participation of the person concerned.
There is also the idea of resurrection, where people are raised from the dead to live again some time after their death. This is an idea that is seen through the Bible. In the period shortly after someone has died, resuscitation seems a reasonable step, and this would be a form of resurrection. With the science of cryogenics, people are hoping that one day this will be open to science. The Bible, however, speaks of a far more powerful resurrection - of people who have been long dead.
Although people working in the biological sciences have looked for ways of significantly prolonging a person's life, this has remained well outside the realms of possibility. This raises two issues. One is that the potential benefit from a faith that offers a resurrection is very high. It is something that we would not be able to attain by any other means. The other issue is that doubt can be cast on the possibility of it, simply because it is not something that is seen day to day.