We study the particle energy distribution in the cocoon surrounding Cygnus A, using radio images between 151 MHz and 15 GHz and a 200 ks Chandra ACIS-I image. We show that the excess low frequency emission in the the lobe further from Earth cannot be explained by absorption or excess adiabatic expansion of the lobe or a combination of both. We show that this excess emission is consistent with emission from a relic counterlobe and a relic counterjet that are being re-energized by compression from the current lobe. We detect hints of a relic hotspot at the end of the relic X-ray jet in the more distant lobe. We do not detect relic emission in the lobe nearer to Earth as expected from light travel-time effects assuming intrinsic symmetry. We determine that the duration of the previous jet activity phase was slightly less than that of the current jet-active phase. Further, we explain some features observed at 5 and 15 GHz as due to the presence of a relic jet.