Now, I've got this theory that is already basically accepted among believers of JCF, but here it is in my own words. Take a look!
The inferior function is of course in direct opposition to the dominant function. When you are under intense stress or rather, "in a funk" and feeling out of sorts (you have probably heard it referred to as being "in the grip"), it can often be explained by your inferior function. Similarly, if your dominant function is starved/stifled, your inferior function will have no choice but to come out and take control. Since your inferior function is so under developed, its emergence can cause the user much angst and confusion, or anger and annoyance, depending on the person and the function.
My question to you is this: What is your inferior function, and how does it manifest?
For example: My inferior function is Ni, and in my case (and I'm sure a lot of you feel the same way), my inferior function is SEVERELY underdeveloped to the point that I'm not even entirely sure what it does or what use I have for it. Recently, I quit both my jobs in restaurants for a cushy cubicle job while I attended community college. Well, lo and behold, sitting on my ass all day, first in a classroom and later in a cubicle, quickly drove me bonkers. Turns out, my Se requires me to have an active job where I can move around a lot and interact with people, face-to-face. In my brief stint as a call center representative, my Se was so starved that I started having horrible, existential thoughts. I started questioning everything I had always accepted at face value to be true. I started thinking more abstractly, which did not agree with me in the slightest. My mind is just not meant to work that way. Physical activity and interpersonal interaction is important to my state of mind for many reasons, mainly just keeping me occupied and sane.
Have you ever had an experience like this?
My brother in law says that under the influence of his inferior Se, he becomes overly sensitive to external stimuli, particularly noises. You see, he is perfectly comfortable pondering the meaning of life or theorizing about God knows what. He is accustomed to abstract thought, therefore it doesn't make him uncomfortable. However, he doesn't work under pressure as well as I do, and he is easily distracted by external stimuli when he is stressed. He is not stimulated by settings that are thrumming with activity like I am. He needs to work in silence and solitude.
My sister and girlfriend both have inferior Te, and I have seen it happen to both of them. They are usually easy going and open minded, but under stress become dogmatic and critical.
My mother has inferior Si. She is usually whimsical and carefree, but under stress becomes very anal and overly attentive to minor details.
My father has inferior Fe. He is usually detached and logical, but under stress becomes clingy and needy.
So in conclusion, it seems that under stress, people are likely to behave quite contrary to the way they would usually behave, and it is not a pretty sight. I'm not entirely sure how we are supposed to "develop" our inferior functions, besides through age and experience, but it seems like a useful thing to do. It might make life a lot simpler.