We present the initial conditions for a decaying cosmological perturbation and study its signatures in the cosmic microwave background anisotropies and matter power spectra. An adiabatic decaying mode in the presence of components that are not described as perfect fluids (such as collisionless matter) decays slower than in a perfect-fluid dominated Universe and displays super-Hubble oscillations. Wilkinson Microwave Anisotropy Probe first year data constrain the decaying to growing ratio of scale invariant adiabatic fluctuations at the matter-radiation equality to less than 10%.