In order to relate the observed evolution of the galaxy stellar mass function and the luminosity function of active galactic nuclei (AGNs), we explore a coevolution scenario in which AGNs are associated only with the very last phases of the star-forming life of a galaxy. We derive analytically the connections between the parameters of the observed quasar luminosity functions and galaxy mass functions. The (mbh/m*)Qing associated with quenching is given by the ratio of the global black hole accretion rate density (BHARD) and star formation rate density (SFRD) at the epoch in question. Observational data on the SFRD and BHARD suggest (mbh/m*)Qing ∝ (1 + z)1.5 below redshift 2. This evolution reproduces the observed mass-luminosity plane of Sloan Digital Sky Survey quasars, as well as the local mbh/m* relation in passive galaxies. The characteristic Eddington ratio, λ*, is derived from both the BHARD/SFRD ratio and the evolving L* of the AGN population. This increases up to z ∼ 2 as λ* ∝ (1 + z)2.5, but at higher redshifts, λ* stabilizes at the physically interesting Eddington limit, λ* ∼ 1. The new model may be thought of as an opposite extreme to our earlier coevolution scenario in Caplar et al. The main observable difference between the two coevolution scenarios, presented here and in Caplar et al. is in the active fraction of low-mass star-forming galaxies. We compare the predictions with the data from deep multiwavelength surveys and find that the "quenching" scenario developed in the current paper is preferred.