In hinduism and buddhism i believe.It is a symbol for leaving behind or rejecting worldly desires. I don't see Beren quite there...It is an old sign of mourning when done to oneself willingly. It is quite dramatic and visible from afar. It is a self-humilation to show one's current situation in society as a mourning person with its tabus and special rights.
If i look for indian barrow burial customs i read things like putting up a special looking stone, drinking to the journey of the deceased, or leaving a bowl of food for him to strengthen him for the journey. Some of that i think could fit for a culture like the Edain...