We report on Chandra grating spectra of the stellar-mass black hole GRS 1915 105 obtained during a novel, highly obscured state. As the source entered this state, a dense, massive accretion disk wind was detected through strong absorption lines. Photoionization modeling indicates that it must originate close to the central engine, orders of magnitude from the outer accretion disk. Strong, nearly sinusoidal flux variability in this phase yielded a key insight: the wind is blueshifted when its column density is relatively low, but redshifted as it approaches the Compton-thick threshold. At no point does the wind appear to achieve the local escape velocity; in this sense, it is a "failed wind." Later observations suggest that the disk ultimately fails to keep even the central engine clear of gas, leading to heavily obscured and Compton-thick states characterized by very strong Fe K emission lines. Indeed, these later spectra are successfully described using models developed for obscured active galactic nuclei (AGNs). We discuss our results in terms of the remarkable similarity of GRS 1915 105 deep in its "obscured state" to Seyfert 2 and Compton-thick AGNs, and we explore how our understanding of accretion and obscuration in massive black holes is impacted by our observations.