Morir de pena

Morir de pena
 

I thought it meant die of shame, but others have informed me that it means die of grief. Could the term have a double meaning? Is there an instance when pena can mean vergüenza?

It depends on the context.


- Me morí de pena cuando me caí frente a todos. -> I was so ashamed, I wanted to die.
- Me muero de pena cuando recuerdo a mi perro que se murió la semana pasada. -> My sadness is killing me.

Gracias como siempre.