Yes you can die in your dreams, while it is rare.
Note: The meanings are based on how you feel in your dream, not just the dying itself.
Die
To dream that you die in your dream, symbolizes inner changes, transformation, self-discovery and positive development that is happening within you or in your life. Although [spoil]such a dreams may bring about feelings of fear and anxiety, it is no cause for alarm and is often considered a positive symbol. Dreams of experiencing your own death usually means that big changes are ahead for you. You are moving on to new beginnings and leaving the past behind. These changes does not necessarily imply a negative turn of events.Metaphorically, dying can be seen as an end or a termination to your old ways and habits. So, dying does not always mean a physical death, but an ending of something.

On a negative note, to dream that you die may represent involvement in deeply painful relationships or unhealthy, destructive behaviors. You may feeling depressed or feel strangled by a situation or person in your waking life. Perhaps your mind is preoccupied with someone who is terminally ill or dying. Alternatively, you may be trying to get out of some obligation, responsibility or other situation.