According to the Faction Guide, they're at least generally brought back via Raise Dead.
"1 TPA, 16 CPA: Be raised from the dead by raise dead. Because of the unique role this ritual has with the Risen Guard, a slain guard can benefit from this reward even if he doesn’t have the CPA or gp to pay for it, in effect going into debt and repaying the cost once he is alive again (an exception to the rule that the Risen Guard are freed from the debts of their past lives). Until this debt is paid, all earned PA and wealth (other than a meager amount for food and clothing) goes to pay it. Likewise, any PA gained does not affect the character’s TPA until the debt is paid. If the character is not actually a Risen Guard when he chooses to use this resource, he becomes one and is thereafter part of the organization—there is no “opting out” of being a Risen Guard, perhaps other than dying and arranging to have some agency other than the Forthbringers raise the character."
The relevant section can be found in the Pathfinder Society Field Guide pg. 18
"Risen Guard (Fame 20, 8 PP) You may voluntarily be killed and resurrected, becoming one of the Ruby Prince’s elite Risen Guard. If you die in the course of an adventure and have not yet purchased this title, you may purchase it to be raised from the dead at this lower price—any future expenditures of PP to be restored from death cost the normal PP amount, as listed on page 3. While your primary mission as such is to protect the royal family, the Ruby Prince recognizes your particular strengths and orders you to protect his interests abroad as a Pathfinder. As a Risen Guard, you may use the honorific “the Risen” after your name. You gain a +2 bonus on Fortitude saves made against death effects and on saves made to prevent a negative level from becoming permanent. Once you gain this prestige award, you can never change your faction."
bolded the relevant section to answer your question.