It's important to keep in mind that bitcoin only has value in the sense that people give value to it. If merchants/users/etc. all decided that particular bitcoins with whatever characteristics (sending address, has a particular pattern of digits in it, whatever) were no longer valuable, and set their wallets, websites, brains, and whatnot to not treat those payments as having any value, then they wouldn't have value anymore.

I find such a scenario pretty unlikely, though.