From Prim's point of view-
Peeta died in the arena. Blood poisoning claimed him before before Cato could. I was both relieved that he was spared from his unmerciful death at the hands of Cato, and sad that he wasn't able to go home. If anyone in that arena deserved to win, it was him. Cato ended up winning the games that year and became one of the most adored victors in Hunger Games history.
Katniss and my mother grieve for sometime after my death, but eventually they get on with life. A funeral procession carries my body to the meadow by the Victors Village. I was buried under a willow tree that overlooks the surrounding forests.
Years and years pass and the day comes when Katniss can think of me without breaking down in tears. She finds comfort in the arms of Gale and the two get married and have a lovely ceremony in the meadow close to the willow tree. Katniss wanted it here because she knew I would have wanted to see her in such a beautiful gown.
I now know I could never have won the games. You have to lose yourself to hurting innocent people; something that is much worse than death. I would be consumed with guilt if I had won the games.
Now, instead of feeling guilt or sadness, I will forever be at peace, deep in the meadow under the willow.