Eeekkk... that looks serious. Time to see the vet. - Blu
It appears to be an abscess and quite a bad one. What you can do in the meantime is use 3% hydrogen peroxide on it to clean it out. With it being that large though just the hydrogen peroxide won't do much other than simply cleaning it so it (hopefully) doesn't get any worse in the time being. They need to take it to a vet so it can get antibiotics and proper treatment.
An abscess is formed when the animal gets scratched or bit and the bacteria from the other animal stays inside the wound. The body naturally heals itself up but because there is still foreign bacteria inside the wound white blood cells are sent to fight it which creates a build up of puss inside the wound. It builds up until it eventually pops, in this case it has already popped. A small abscess can potentially be treated at home by just cleaning it out regularly so when it heals over again the bacteria inside is gone allowing the body to heal correctly. But like I said with it being this big they must take it to a vet for proper cleaning and medications.
Omg, I have no idea, but the sooner your cousin gets this bunny to a Vet, the better! I will be honest and say, I've never seen an abscess before, so *maybe*.
Please forgive me, but I am having a hard time telling what part of the bunny I am looking at???