Episode 4 of "Without a Trace"
s01e04 Between the Cracks

The agents' job is harder than usual: they must find a woman, Eve, who changes her appearance to suit whatever modeling or acting job she is seeking at the time. No one seems to know Eve well, including her roommate, who filed the missing persons report when she notices that Eve's beloved cat has not been fed for days. Jack and the team find a half-packed suitcase in Eve's room but few other clues. The investigation becomes more illuminating when the squad members interview people associated with the modeling agency that Eve occasionally worked for. Meanwhile, Jack is haunted by an old case that he still cannot solve for grieving father Chet Collins.