Syllogistic Rule Violated:
In a validating form of categorical syllogism, any term that is distributed in the conclusion is distributed in the premiss in which it occurs.
An illicit process is not an illegal trial. Rather, it is a fallacy committed by any argument of the form of a categorical syllogism that has a term distributed in the conclusion but not in the premiss in which it occurs. Since every categorical proposition has two terms, this means that there are two subfallacies of this fallacy―see above―depending upon whether it is the major term or the minor term which is illicitly distributed. Every categorical syllogism that commits the fallacy of illicit process also commits at least one of its subfallacies, depending on which term is distributed in the conclusion. Some forms of categorical syllogism have both an illicit major and minor terms, but arguments with these forms are so implausible that it's unlikely anyone would be fooled by them. For examples of illicit process, see the subfallacies.
Most discussions of syllogistic fallacies do not mention illicit process as a separate fallacy, but discuss only its two subfallacies. However, both subfallacies commit the same mistake―the "illicit process"―in that a term that is undistributed in a premiss is distributed in the conclusion.
*Note: See also: Irving Copi & Carl Cohen, Introduction to Logic (Tenth Edition) (Prentice Hall, 1998), pp. 276-7.