It is widely acknowledged that inhaled fibers, e.g. air pollutants and anthropogenic particulate matter, hold the ability to deposit deep into the lungs reaching the distal pulmonary acinar airways as a result of their aerodynamic properties; these particles tend to align with the flow and thus stay longer airborne relative to their spherical counterpart, due to higher drag forces that resist sedimentation. Together with a high surface-to-volume ratio, such characteristics may render non-spherical particles, and fibers in particular, potentially attractive airborne carriers for drug delivery. Until present, however, our understanding of the dynamics of inhaled aerosols in the distal regions of the lungs has been mostly limited to spherical particles. In an effort to unravel the fate of non-spherical aerosols in the pulmonary depths, we explore through numerical simulations the kinematics of ellipsoid-shaped fibers in a toy model of a straight pipe as a first step towards understanding particle dynamics in more intricate acinar geometries. Transient translational and rotational motions of micron-sized ellipsoid particles are simulated as a function of aspect ratio (AR) for laminar oscillatory shear flows mimicking various inhalation maneuvers under the influence of aerodynamic (i.e. drag and lift) and gravitational forces. We quantify transport and deposition metrics for such fibers, including residence time and penetration depth, compared with spherical particles of equivalent mass. Our findings underscore how deposition depth is largely independent of AR under oscillatory conditions, in contrast with previous works where AR was found to influence deposition depth under steady inspiratory flow. Overall, our efforts underline the importance of modeling oscillatory breathing when predicting fiber deposition in the distal lungs, as they are inhaled and exhaled during a full inspiratory cycle. Such physical insight helps further explore the potential of fiber particles as attractive carriers for deep airway targeting.