The contact binary Kuiper Belt object (486958) Arrokoth, targeted by New Horizons mission team, has a unique slope pattern, which is a result of its irregular bilobate surface shape and high spin period. Thus, some peculiar topographic regions on its surface are predisposed to accumulate or lose material as a large circular depression feature, an impact crater called Maryland, on its small lobe and the LL_Term area on its large lobe. The structure of the phase space near these surface features is also directly connected to the saddle equilibrium points of Arrokoth. Thus, we performed long-term numerical simulations around Arrokoth to explore the fate of particles close to its four unstable equilibrium points and their dynamical connection with its surface features. Our results suggest that most of these particles in a ring inside the Arrokoth’s rotational Roche lobe fall back across its surface near the equatorial region of the Maryland crater or close to the Bright spots equator areas on the large lobe. In contrast, few of them fall back near the LL_Term equatorial region. Also, particles in a spherical cloud orbiting Arrokoth preferentially fall near low-mid-latitudes regions close to longitudes of Maryland crater and Bright spots areas. The high-latitudes are those more depleted of falls, as in Pits sites. Additionally, particles smaller than a micron are quickly removed from the Arrokoth’s environment by solar radiation pressure, while particles larger than few microns are dominated only by the irregular gravity field of Arrokoth.