Elementary particles That's what Wikipedia says about Elementary Particle:

In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is not known to be composed of other particles.

Assumed the above sentence: 
Can we ever know the structure of an elementary particle "Z" if it is an agglomeration of other n sub-particles "T" that, toghether, cancel their actractive forces creating our singular Z particle?
An answer could be to collide 2 "Z" particles until they break and show us the "T" particles, but again, the same question can be formulated for the "T" particle. We can demonstrate that a particle is not elementary, but we can't say that it is NOT composed of other particles.
This leads to another concept:
suppose we make and demonstrate an M-Theory called "X" which affirm that "n" different particles can stick making all other known particles with the same known properties  , we're not able to demonstrate that there's no other M-Theory "Y" that generalize the "X" one.
Furthermore can even make sense to formulate tens of different "Y" M-Theories which logically generalize the "X" one and that, simulated on a utopian machine, generate the "X" environment. 
The core question is, will we ever know when we are done?
 A: 
The core question is, will we ever know when we are done?

Simple answer: no. Physics is an experimental science, so is wholly reliant on inductive reasoning. Simply put: you can only prove something is true by observing it, but you cannot prove something is not true by not observing them. You can only gather evidence that something is not true by trying to observe it yet failing to do so. Even deeming something observed to be true is not foolproof: our observations are always uncertain and so what is actually happenning in an experiment can always be subtly different from what we believe we are observing.
Your fundamental particle example is a very good example of this. We simply believe certain particles are fundamental because either (1) we have tried to break them apart, but we've never seen them break apart or (2) their quantum state space and the way their states transform under boosts, rotations and other symmetries have certain hallmarks of a "fundamental particle" (the state behaves as though an image of an irreducible representation of the symmetry group) and when we do calculations with this model, we get results that are in keeping with experimental observations.
Actually (1) is sometimes a little more subtle than I have quoted. For quarks, we know they are there from deep inelastic scattering experiments, which is essentially the Rutherford experiment done with nucleusses rather than gold atoms. So far, the same kind of experiments have given no evidence of anything within quarks as these experiments' energies increase (and therefore their probing resolution becomes finer).
A: Well it turns out that all particles in the standard model are maybe made of particles called "preons". However this is not a well supported theory. The theory that is trying to answer what particles are really made of is string theory. They say that all particles are made of one dimensional "strings".
