We consider a resource sharing model for $N$ financial firms which takes the form of a semimartingale reflected Brownian motion in the positive orthant. When the asset value of any firm hits zero, the other firms contribute to a local time reflection term to keep the distressed firm's assets non-negative. Depending on a critical parameter $\alpha$, which reflects either friction or subsidy, the interval of existence for this scheme is shown to be either infinite, or almost surely finite. In the mean-field limit, the behaviour of the Fokker--Planck equation also depends on $\alpha$: either solutions exists for all time or the equation exhibits finite-time blowup. The passage from finite to mean-field model is investigated. We also analyze connections between our model and systemic risk models involving hitting times, the up-the-river problem of Aldous, various free boundary PDEs, and Atlas models from Stochastic Portfolio Theory.