DYE is a homophone of DIE. Homophones are words that are pronounced the same by they are different in meaning or spelling.
Is Samantha was in a good mood, probably she is likely to think that they are going to the hairdressers to have the hair dyed because it has turned grey or because they want to change the colour.
In a more pessimistic situation, she was likely to think that they were talking about death.
