Just a year ago, Ms. Brannigan, 24, who holds up Case No. 24 as one of the models on the NBC game show “Deal or No Deal,” had been full of hope when she and her fiancé had each other’s names tattooed across their inner wrists.

But now, when she looks at the letters — P-A-T-R-I-C-K — she is reminded of the failed relationship.