- It would be good to specify what "majority of radiation" means. If it means "radiative energy", then this premise is surely wrong. To find the energy emitted per wavelength, take the Planck function $B(T, \lambda)$ at a certain temperature $T$ and multiply with the wavelength $\lambda$. You will find that the short-wavelength radiation always dominates for a black-body.
- Wien's law gives you the peak of the Planck function. Radiation at all other wavelengths exists.
Note that objects predominantly loose most of their energy, if photons and matter are in equilibrium. If this equilibrium is disturbed, or particle accelerations play a role (like in the presence of magnetic fields), a whole zoo of non-thermal processes can also lead to important radiative energy loss.
Non-thermal processes in space can be radio emission from gyrating particles, line radiation, Masers, Bremsstrahlung, Compton radiation... Those processes then do not show a Planck spectrum, but other characteristic spectra.
Edit: I've added a plot of the Planck function at two different temperatures. In a linear plot (on the left) it might look as if there's a cut-off, but in a logarithmic plot (on the right), one sees what mathematical analysis already betrays: The function is defined everywhere. It just becomes really small on the high-energy end, as a commentator pointed out correctly.