This is a speculation. And it goes a little something like this:
The tertiary function--relief--we turn to it to find energy for and the recharging of whatever our higher functions are about. (Also we turn to it to let the pressure out of the demands of our higher functions, but that's another story.) And being relatively underdeveloped and less conscious than the higher functions, the relief function produces simple-minded demands about how things ought to be.
Take INTJs for instance. I know that having Fi under Te tends us toward simple-minded demands that other people have their moral compass on straight. "You will treat me with respect and you will know what respect is!"--that kind of thing. Vocalising about moral requirements. "You're going the wrong way! You're making the wrong choice! What do you really want!" And so on. It's odd, but it's true. "Everything will go better if the feeling is right, or I'm outta here!" If you look around the forum, you can see INTJs doing it all over the place.
So I have come to wonder, what does having Te under Fi do in ENFPs? Well, it's Te, so it'll be something about how the world will be organised; and it's in service of Ne/Fi, so...
The ENFP Te demand: "the world will be organised in such a way that people can interact and be at risk because I need them to take risks."
("And I'll be really sorry if you get hurt, but it's not my fault if you do get hurt because that's just the way the world is, you have to be responsible for yourself.")
Like I say, the demands imposed by the relief function are relatively simple-minded, and looked at in isolation, they sound awful, but the higher functions are there to take up the slack and balance out the awfulness. Like for example, ENFPs having Ne/Fi will be able to say, yeah, people are at risk, but I'm sympathetic and empathetic and I can be trusted not to hurt you. INTJs back up their Fi demand by saying, I will stand fast to my moral criterion and meanwhile I'll be organising the shit out of everything else so if you know what you want, you don't have to worry about me not knowing about everything else.
This is a first draft, it's a nice draft, but I don't know if it's a true draft. A lot of the claims might be wrong in expression and might need some whittlin'. What say you?