The purpose of subnormal numbers is not to avoid underflow/overflow entirely, as some other arithmetic models do. Rather, subnormal numbers eliminate underflow as a cause for concern for a variety of computations, typically, multiply followed by add. For a more detailed discussion, see Underflow and the Reliability of Numerical Software by James Demmel and Combating the Effects of Underflow and Overflow in Determining Real Roots of Polynomials by S. Linnainmaa.
The presence of subnormal numbers in the arithmetic means that untrapped underflow, which implies loss of accuracy, cannot occur on addition or subtraction. If x and y are within a factor of two, then x – y is error-free. This is critical to a number of algorithms that effectively increase the working precision at critical places in algorithms.
In addition, gradual underflow means that errors due to underflow are no worse than usual round-off error. This is a much stronger statement than can be made about any other method of handling underflow, and this fact is one of the best justifications for gradual underflow.