At arbitrary prices of commodities and assets, fix-price equilibria exist under weak assumptions: endowments need not satisfy an interiority condition, utility functions need only satisfy a very weak monotonicity requirement, and the asset return matrix allows for redundant assets. Prices of assets may permit arbitrage. At equilibrium, though restricted through endogenously determined trading constraints, arbitrage possibilities may persists in an example, an individual holds an arbitrage portfolio.
Herings, P. J. J., & Polemarchakis, H. M. (2002). Equilibrium and Arbitrage in Incomplete Asset Markets with Fixed Prices. Journal of Mathematical Economics, 37, 133-155. https://doi.org/10.1016/S0304-4068(02)00013-7