The very high energy (VHE; E > 100 GeV) blazar Markarian 501 has a well-studied history of extreme spectral variability and is an excellent laboratory for studying the physical processes within the jets of active galactic nuclei. However, there are few detailed multiwavelength studies of Markarian 501 during its quiescent state, due to its low luminosity. A short-term multiwavelength study of Markarian 501 was coordinated in March 2009, focusing around a multi-day observation with the Suzaku X-ray satellite and including {gamma}-ray data from VERITAS, MAGIC, and the Fermi Gamma-ray Space Telescope with the goal of providing a well-sampled multiwavelength baseline measurement of Markarian 501 in the quiescent state. The results of these quiescent-state observations are compared to the historically extreme outburst of April 16, 1997, with the goal of examining variability of the spectral energy distribution between the two states. The derived broadband spectral energy distribution shows the characteristic double-peaked profile. We find that the X-ray peak shifts by over two orders of magnitude in photon energy between the two flux states while the VHE peak varies little. The limited shift in the VHE peak can be explained by the transition to the Klein-Nishina regime. Synchrotron self-Compton models are matched to the data and the implied Klein-Nishina effects are explored.