In chapter 12, John and Lorraine confess to Mr. Pignati that they are not members of the "L & J Fund" afterall. Their guilt has gotten the better of them as they have grown to care for Mr. Pignati and they feel they owe it to him to be honest. He reciprocates their honesty by admitting that Conchetta is in fact dead, and not vacationing in California with his sister, as he had originally told Lorraine and John.
In the book "The Pigman John and Lorraine are teenagers who lack self focus and responsibility. They unexpectedly become friends with Mr. Pignati, a widower who pretends his wife is still alive and visits the baboon Bo Bo at the zoo regularly. He is very lonely and becomes excited to have friends and generous with the young teens.
I found no mention of the teens confessing to Mr. Pignati until the later chapters. The kids had friends over to Mr. Pignati's home while he was in the hospital. The party got carried away and the students had destroyed some of his prized possessions and Lorraine and John had worn his and his wife's clothing. Mr. Pignati was devastated when he returned home early from the hospital and saw the scene.
The two teens had learned how badly they had hurt him and they apologized and tried to get him to let them see him. On page 137 they apologize for having the party.