The Black model was presented by Fischer Black in a 1976 paper. It replaces the stock price in the Black-Scholes model with a forward price. Under the model, the forward rate follows a lognormal distribution and does not take values at or below zero.
For this reason, the model cannot produce a price when the forward rate is at or below zero. When interest rates were negative, the Bachelier model, which assumes that the forward rate itself follows a normal distribution, came into wide use.