But things are getting interesting now.
Mass in a closed system doesn't change and neither does energy you say.
Let us imagine the following:
A closed system with a mass m and an energy of m*c^2 + E0. E0 is the amount of energy present in the system which isn't located in the mass. (radiation, heat and stuff)
Now we make sure that E0 equals zero. We do this by isolating the system to get rid of radiation and putting the system in the superfreezer to get the temperature at 0 degrees Kelvin.
We measure the mass of the system and get 1 kilo.
Then we do nothing with it for several thousand years.
After all these thousands of years have gone we measure the mass of the system again.
The mass hasn't changed you say so it still is 1 kilo. The energy hasn't changed either you say so that is still m*c^2 + E0. Since the system has been isolated from radiation and it has been in the freezer all these thousands of years, E0 is still 0.
Now you may explain to me how c can have changed.