We analyse field fluctuations during an Ultra Slow-Roll phase in the stochastic picture of inflation and the corresponding non-Gaussian curvature perturbation, fully including the gravitational backreaction of the field's velocity. By consistently working to leading order in a gradient expansion, we first demonstrate that the momentum constraint of General Relativity prevents the field velocity from having a stochastic source, unlike what a naîve application of the separate universe picture might seem to suggest. We then focus on a completely level potential surface, V=V0, extending from a specified exit point ϕe, when slow roll may resume or, alternatively, inflation ends, to ϕ→+∞. We compute the fluctuation in the number of e-folds N required to reach ϕe, which directly gives the curvature perturbation. We find that, if the field's initial velocity is high enough, all points exit through ϕe and a finite curvature perturbation is generated. On the contrary, if the initial velocity is low, some points enter an eternally inflating regime despite the existence of ϕe. In that case the probability distribution for N, although normalizable, does not possess finite moments, leading to a divergent curvature perturbation.
