What is the importance of Piggy's character, role, and death in chapters 8-10 of Lord of The Flies?

Piggy is highly significant to the thematic development in Lord of the Flies.  He embodies the idea of law and order, rational thought, and striving to be honorable in a dishonorable time. Piggy represents the constructive aspect of civilization, a progressive attitude that becomes the minority and eventually is silenced through the forces of power and control.  His marginalization and eventual death reflects how social conformity and the desire to appropriate the world in accordance to one's own subjectivity can eliminate voice.  This is seen throughout the book, but specifically in eight through ten.

"The Beast" is a symbol that is used to generate power and control. Its presence lends credence to Jack's claims to power and that the boys must embrace a defensive and militaristic approach than a more legislatively rational one.  When Ralph becomes convinced of the Beast, it is evident that Piggy is moving towards even greater marginalized status. Piggy's desire for answers, involving a careful and methodical approach to understanding how the reality of the beast is constructed, is what Jack calls "poor leadership."  It is at this moment in chapter 8 where it is clear that Piggy's voice of reason is seen as weakness and threatening to the condition of Jack's hunters. When Piggy loses Ralph, his chief protectorate and ally, it is clear that his time is evaporating quickly.  In an act of desperation, Piggy tries to rally the boys' attention in building a fire to scare off the beast:  “The boys began to babble. Only Piggy could have the intellectual daring to suggest moving the fire from the mountain.”  As the anarchy descends upon the island, where the center of progressive reason cannot hold, Piggy is one of the sole believers in rationality, civilization, and "acting like adults."

The movement of Piggy to the fringes of the social order on the island reflects how he becomes an easy target to others.  Piggy becomes the outsider.  In a world where there is no structure, his belief in one helps to doom him.  When Piggy is burned by one of the boys, his physical hurt causes the boys to laugh at him:  "Piggy once more was the center of social derision so that everyone felt cheerful and normal.” Feebly, Piggy tries to join Ralph and the other boys as a means of inclusion, but it is evident that there is something larger at play, "another desire, thick, urgent, blind.”  At this point, Piggy's characterization shows how the devolution of social order is going to demand victims.  Piggy, who is not athletic, portly, intellectual, and asthmatic is a prime target.  The demonstration of Piggy as an outsider who retains his intrinsic qualities while trying to conform is reflective of this "thick, urgent, and blind" condition which makes his escape impossible.  His conformity led to the mass killing of Simon.  Piggy's participation renders him helpless.  In the critical moment of action, he betrayed his progressive and rational principles, and as a result, his own sense of identity becomes absent.

Through this assimilation, it is clear that Piggy will not last the coming storm.  His use of rationalization in Simon's death is reflective of his personality and temperament, but in the end, there is little he can do to offset that which seems inevitable.  His longing for the past and the lack of affect from the others is a reflection of how little time is left for him:  "I don’t know where she [Piggy's aunt]  is now. And I haven’t got an envelope and a stamp. An’ there isn’t a mailbox. Or a postman.”  The basic semblance of order and logic that had dominated his world and his being are eroding, akin to the structure of the social organization on the island.  The stealing of Piggy's glasses causes a loss of vision both literally and metaphorically.  It is at this point where Piggy's loss and marginalization is reflective of how society targets those on the outside with precision and accuracy in its desire to silence voice.  Piggy embodies this in his interactions with the boys on the island, specifically evident in chapters 8 through 10.

What is the symbolism of Piggy, Simon, and the airman being carried out to sea in Lord of the Flies?

Piggy, Simon, and the airman being washed out to sea is a religious symbol of rebirth.

Burial at sea is often considered going back from whence we came.  When a character crosses through water in a book, it is often symbolic of baptism or rebirth.  In this case, the characters are freed and reborn by being washed out to sea.

The airman represents civilization and the adult world.  It is the boys’ one connection to the word they came from, and it washes away.  This demonstrates the change in the boys’ society from civilized to uncivilized.

When Simon is washed out to sea, it is because he is attacked by the gang pretending he is the pig.  He is the beast to them.  In reality, Simon is the prophet, the innocent being who is sacrificed in a Christ-like way.  When Simon convenes with the Lord of the Flies “pig’s head on a stick,” he realizes that the beast is inside all of them.

“Fancy thinking the Beast was something you could hunt and kill! ...You knew, didn’t you? I’m part of you? Close, close, close! I’m the reason why it’s no go? Why things are what they are?” (ch 8)

When Simon goes to tell the others and warn them where the beast is, they kill him—mistaking him for the beast itself.

Piggy is sacrificed more intentionally. He represents civilization with his glasses and his brains.  His thought processes are of the world they came from.  When stealing his glasses for fire does not work, they roll a boulder on top of him and his boy is washed out to sea.  At this point the men show up to rescue them, with the boys being reborn from his sacrifice.

Why is Piggy an important symbol and what is Simon's significance in "Lord of the Flies"?

Piggy and Simon are important characters not just for the development of the plot of Lord of the Flies but also as characters who represent a larger concept. Piggy represents intelligence and technology, but he also represents marginalized people who are easily victimized in a less enlightened society. Piggy is by far the most intellectually superior boy on the island. He is the one who has the idea to call the other boys with the conch, and he alone has the "intellectual daring" to consider building the signal fire on the beach when the "beast" prevents them from tending it on the mountain. His glasses symbolize intellect but also science and technology; they give the boys the ability to create fire. Still, Piggy is mocked and bullied by the boys, especially Jack. Because Piggy has asthma and is overweight, Jack chooses him to pick on, often telling him to shut up and charging into his stomach and breaking his glasses.

Simon represents the sensitive, insightful, or spiritual person or part of society. Like the other easily victimized people, spiritually sensitive people are often dismissed and/or ridiculed by many people in a society. The boys often remark that Simon is "batty" or "crazy." Simon is the one who recognizes "mankind's essential illness" and suggests about the beast that "maybe it's only us." This earns him scorn. When he has a vision of the Lord of the Flies, it confirms what he has already discerned, namely that the "beast" is the tendency toward evil that resides inside every person. Unfortunately, Simon's revelation is not useful to any of the other boys; they end up killing him before he can get them to understand. In this way Simon is a Christ-figure; he is killed by those he is trying to enlighten.