  We study the dissipative Rabi model under deep strong far-off-resonant
driving when the driving frequency and strength exceed significantly the qubit
transition frequency. We find analytical expressions for the density matrix,
the steady-state first-order field correlation function and the multiphoton
emission spectrum. This spectrum consists of a series of narrow delta-like
lines, caused by coherent processes and of Lorenzian peaks resulted from the
incoherent scattering of photons. It is shown that the width of emission lines
as well as the decay rate of the time oscillations in the population difference
have oscillating dependence on the driving strength. We show how the features
of this dependence are controlled by the relative rates of energetic relaxation
and pure dephasing.
