Literature
Loving Those Who Overthink or Are Depressed
Loving Those Who Overthink, Are Depressed, or Hate Themselves
(Or a Guide to Handling Your Cupcake)
1) No matter how many times it's necessary, argue. Every time they vent about how hideous, worthless, or moronic they think they are, fight it. Day in and day out, no matter how much they don't believe you, they still want to hear it. They need it, but they won't ask for it.
Maybe once and a while you don't want to start a full on debate. Simply tell them, if they don't tell you, that you don't want to fight again. Just tell them they already know you think they are amazing and move on to talk about more pleasant things.
2) Try not to leave