If you saw Pyramus's "Character Analysis," you won't be surprised to hear that we don't know much about Thisbe, either. Just like her beau, all that we know about her is that she's young and in love. She's also an archetype, around to represent a type of person, not a fully fleshed-out character.
Don't get us wrong, though. We're not saying Thisbe is cliché. Instead, we look at her as the inspiration for so many other characters to come. You've heard of a girl named Juliet, right? Yeah, this is where Billy Shakes got the idea from. Just like Shakespeare's Juliet, Thisbe is so overcome with grief at her lover's mistaken suicide that she kills herself as well.
In the end, she's destroyed by her overpowering love and the hatred that kept her and Pyramus's families apart. Double whammy.