Over its lifespan, the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will monitor millions of supernovae (SNe) from explosion to oblivion, yielding an unprecedented ugrizy photometric dataset based on their late-time evolution. Here, we show that the photometric evolution of Type Ibc SNe can be used to constrain numerous properties of their ejecta, without the need for expensive spectroscopic observations. Using radiative-transfer simulations for explosions of He-star progenitors of different initial masses, we show that the g-band filter primarily follows the strength of the Fe II emission, the r-band [O I] lambda lambda 6300, 6364 and [N II] lambda lambda 6548, 6583, the i-band [Ca II] lambda lambda 7291, 7323, and the z-band the Ca II lambda lambda 8498 - 8662 triplet, hence providing information on nucleosynthetic yields. Information on weaker lines that may be used, for example, to constrain clumping is absent. However, this deficiency may eventually be resolved by improving the physical realism of radiative-transfer simulations through a closer connection to physically consistent 3D explosion models, as well as through the judicial selection of a much smaller set of spectral observations. Degeneracies inherent to the SN radiation will affect the interpretation of photometric measures, but line fluxes from nebular-phase spectra are similarly compromised. Importantly, our "family" of Type Ibc SN models follows a distinct trajectory in color-color magnitude diagrams as the ejecta evolve from 100 to 450 d, allowing for the disentanglement of different progenitors or explosions. This photometric procedure provides a promising approach to studying statistical samples of SNe Ibc and confronting them with consistently improving progenitor and explosion models, as well as capturing the onset of late-time interaction with circumstellar material or identifying events currently unknown.