You might also be thinking of Logan's Run, wherein a crystal set in each person's palm changes color every few years, and starts blinking at 21, signalling time for cumpulsory euthanasia. The story concerns those who run away, seeking a place called Sanctuary.
However I don't recall that anyone gets eaten.
In Soylent Green, the dead are recycled into food wafers, but I don't think there was an age limit on living, though euthanasia was highly encouraged.And Soylent Green is the title of a film, which is only loosely based on a book called Make Room, Make Room.