She appears in the desert when Frankie Fusilli asks you to bury a wiggling chest. After you are caught, both the chest and the shovel are removed from your pockets and cannot be bought again. You return to Frankie in the Penthouse in order to complete the task; but once you return to the Town Square; you are acquainted once again with Penelope, she asks you to wear a wire while calming Frankie down in order to gather information. Penelope can be checked in after she's introduced.
Her boss at the FBI hasn't actually told her why she is in Strangetown.