From Wikipedia:
“The nasolacrimal duct (sometimes called the tear duct) carries tears from the lacrimal sac into the nasal cavity. The opening of the nasolacrimal duct into the inferior nasal meatus is partially covered by a mucosal fold (valve of Hasner or plica lacrimalis). Excess tears flow through nasolacrimal duct which drains into the inferior nasal meatus. This is the reason the nose starts to run when a person is crying or has watery eyes from an allergy, and why one can sometimes taste eye drops.”
Without these, the terrifying vision of death cannot cry the way you and I can cry. It could fake it. Stage tears and heavy breathing. But the terrifying vision of death is a very authentic creature.