The evolutionary dynamics of a magnetic neutral sheet are followed using a nonperiodic, two-dimensional magnetoinductive particle-in-cell simulation. The purpose of this study is to observe the effects of particle and field boundary conditions. With open boundary conditions, particles can freely pass the simulation boundaries. Particles leaving the domain are lost forever, while other particles are continually reintroduced from the adjoining reservoirs. The statistical properties (density, flux, scalar pressure) of the reservoir particles, including gradients transverse to the boundaries, are specified. The field boundary conditions are similarly ''open.'' The effect of open boundary conditions on the ion tearing mode instability are studied by comparison with periodic simulations. The results show that there is little difference between the initial time evolution in the periodic and the open systems but that the boundary conditions can have a noticeable effect on the nonlinear phase of the tearing mode, especially on the properties of the magnetic islands. When there are no particles in the reservoir, particles at the ends of the simulation domain escape and an O-type neutral line (magnetic island) is formed. When the reservoir particle distributions are maintained to give the same densities and pressures as existed in the initial distribution the tearing instability leads to the ejection of all the particles from the simulation domain and the almost total collapse of the magnetic field.