Abstract: Given a 4-dimensional Einstein orbifold that cannot be desingularized by smooth Einstein metrics, we investigate the existence of an ancient solution to the Ricci flow coming out of such a singular space. In this talk, we will focus on singularities modeled on a cone over RP3 that are desingularized by gluing Eguchi-Hanson metrics to get a first approximation of the flow. We show that a parabolic version of the corresponding obstructed gluing problem has a smooth solution: the bubbles are shown to grow exponentially in time, a phenomenon that is intimately connected to the instability of such orbifolds.