  We present new Spectrographic Areal Unit for Research on Optical Nebulae
(SAURON) integral-field spectroscopy and Swift Ultraviolet Optical Telescope
(UVOT) observations of molecular outflow host galaxy NGC 1266 that indicate NGC
1266 has experienced a rapid cessation of star formation. Both the SAURON maps
of stellar population age and the Swift UVOT observations demonstrate the
presence of young ($< 1$ Gyr) stellar populations within the central 1 kpc,
while existing Combined Array for Research in Millimeter-wave Astronomy (CARMA)
CO(1--0) maps indicate that the sites of current star formation are constrained
to the inner few hundred parsecs of the galaxy only. The optical spectrum of
NGC 1266 from Moustakas & Kennicutt (2006) reveal a characteristic
post-starburst (K+A) stellar population and Davis et al. (2012) confirm that
ionized gas emission in the system originate from a shock. Galaxies with K+A
spectra and shock-like ionized gas line ratios may comprise an important,
overlooked segment of the post-starburst population, containing exactly those
objects in which the AGN is actively expelling the star-forming material. While
AGN activity is not the likely driver of the post-starburst event that occurred
500 Myr ago, the faint spiral structure seen in the Hubble Space Telescope
(HST) Wide-field Camera 3 (WFC3) Y-, J- and H-band imaging seems to point to
the possibility of gravitational torques being the culprit. If the molecular
gas were driven into the center at the same time as the larger scale galaxy
disk underwent quenching, the AGN might be able to sustain the presence of
molecular gas for $\gtrsim 1$ Gyr by cyclically injecting turbulent kinetic
energy into the dense molecular gas via a radio jet, inhibiting star formation.
