Only three extragalactic supernovae have been detected at late times at millimeter wavelengths: SN 1987A, SN 1978K, and SN 1996cr. SN 1978K is a remarkably luminous Type IIn supernova that remains bright at all wavelengths 40 years after its explosion. Here, we present Atacama Large Millimeter/submillimeter Array (ALMA) observations taken in 2016 using Bands 3, 4, 6, and 7 that show a steepening in the spectrum. An absorbed single power-law model broadly fits all of the radio and millimeter observations, but would require significant chromatic variability. Alternatively, a broken power law fits the radio-millimeter spectrum; this can be explained using an ultra-relativistic spherical blast wave in a wind scaling with a cooling break, as in a gamma-ray burst afterglow. Using updated Australia Telescope Compact Array light curves, we show that the non-thermal radio continuum continues to decay as t−1.53; in the fireball model, this independently defines the power-law indices found in the radio-millimeter spectrum. Supernovae such as SN 1978K might be important contributors to the universal dust budget: only SN 1978K was detected in a search for warm dust in supernovae in the transitional phase (age 10-100 yr). Using Spitzer Space Telescope observations, we show that at least some of this dust emission has been decaying rapidly as t−2.45 over the past decade, suggesting it is being destroyed. Depending on the modeling of the synchrotron emission, the ALMA observations suggest there may be emission from a cold dust component.