There are certainly (short-rate) models which assume bounded interest rates. I suppose I should clarify - the design of the model prohibits negative interest rates. Further, some models asymptotically reach some target, or mean rate which is considered mean reversion, the most famous perhaps the Vasicek.
Short rate models where rates cannot go negative:
Short rate models where rates can go negative:
These are all stochastic models that can be solved in discrete time.
Of course, each of these models have there own shortcomings. For example, the mean reversion in the Black-Derman-Toy model is dependent on volatility decay which only happens in practice if the modeled volatility is fit to traded securities whose volatility diminishes over time.
People may use an interest rate model which has the possibility of negative interest rates if they are valuing derivatives that might have a payoff of 0 when rates get low, or below some low but positive value. In other words, the interesting stuff happens at some high positive interest rate.
For a simple example, think of a put option on a bond. This contract only gets interesting when the price of the bond goes down (with the corresponding rates going up) so it really doesn't matter if the model has negative rates in it because we're only interested in the payoffs when rates are high.