Here are some possibilities of what death, dying or a dead person may represent:
(1) The basic meaning: The old is dying; make way for new beginnings.
(2) Sometimes when death arises in literature, what is really being expressed may be the MC’s own anxiety about dying. Death is inevitable, and facing up to that fact may bring great rewards: self-acceptance; new values; a broadening of one's personality, compensating for past omissions or lopsidedness and utilizing previously neglected personal resources.
(3) When the dying person is the MC’s best friend, parent or sibling, the underlying message may be expressing unconscious resentment towards that character or a desire to be independent of that character. Feelings toward someone close are often ambivalent (conflicting): love or respect mixed with fear or hatred or resentment or jealousy.
(4) If the MC dreams of him/her dead or dying, the message may be that the MC’s old self needs to be left behind. This may mean he/she must stop carrying around the crippling burden of his/her past (irrational guilt-feelings or other negative self-programming); and, instead, he/she must accept what the present moment is offering. Alternatively, the 'old self' may be old attachments, habits, ambitions, values, goals; in which case the dream is portraying that the only way forward for the MC lies through giving these up and looking deeper within him/herself for better values, etc. (where better means more in tune with his/her real self).
(5) A dead animal in a story sometimes refers to some part of the MC — an instinctive force, perhaps — and the author is hinting that this part of the MC (e.g. guilt-feelings or inferiority complex) ought to die, because its effects are wholly negative; or that it is a valuable but repressed part of him/herself that must now be brought to life, to rectify an imbalance in your personality.
There you have it, my take on death in literature. Have you seen the symbol of death used in other ways? If so, share them below.