Good question! Unfortunately, most textbooks, including E&Z, don't mention the fourth type. Its one that Durkheim talked very little about, but that is the logical extention of his theory. The three types of suicide discussed, namely egoistic, anomic, and altruistic, can be seen as three of the four ends of two intersecting axis, where the two axis are regulation and integration. Two little regulation is anomie, too little integration is egoism, too much integration is altruism, and too much regulation is FATALISM. Durkheim was so concerned that due to rapid social change there wasn't enough regulation (he called this condition anomie), that he left out of his discussion the opposite condition: too MUCH regulation. Examples of fatalistic suicide would include prisoners, students in a strict boarding school, or housewives with children in a society with strict male control of women. All would suffer from too little control over their lives, with some responding by taking their lives.

Another point I should make is that Durkheim wasn't really interested in understanding suicide; he only focused on suicide because fairly good data on suicide was becoming available and it allowed him to test his theories about the proper relationship between individuals and social groups. He argued that people need a proper balance of regulation and integration. Too much or too little of each would lead to suffering. One response would be suicide, but the problem wasn't suicide, it was too much or too little integration or regulation (he beleived the main problem Europeans faced was too little regulation, or anomie, due to the rapid rates of social change).

Hope this helps.