In the double-slit experiment, why is it never shown that particles may hit the space between or outside the slits? In depictions of the double-slit experiment that model the photon or electron as a particle, i.e. when attempting to measure which slit the particle passes through, it always shows the particle entering one of the two slits. Why is it that the particle can't hit the space between or outside the slits, i.e. never even make it through? Is it implied that the experiment is just repeated until a particle makes it through, i.e. shows up on the film or detector on the other side?
I see how, modeled as a wave, the wave always makes it through. But the illustrations of particles kind of don't make sense to me. Is it because they are just simplified illustrations?
I realize this sounds like a silly question, but I'm trying to go back and question everything I've taken for granted. (For example, I wondered what if there is some weird, hidden interaction between the ones that didn't make it through and the ones that did?)
 A: "Is it because they are just simplified illustrations?" you ask. The answer is simply: yes it is because they are simplified illustrations.
Furthermore, not only can the particle hit the barrier outside or between the slits, typically most of the particles do that. Only a small fraction make it through. I say 'typically' because in such experiments we don't normally bother to set up the optics (whether for photons or electrons) so as to restrict illumination to only the two slits and not the surrounding area. But in principle it could be done, and then only a few particles would miss the slits.
It is quite common, in experimental physics in this area, to do what is called 'post-selection'. That is the name for the practice of selecting from your dataset only those outcomes triggered by some signal, such as, in this case, the signal that a dot appeared somewhere on the final screen. Then after that the discussion is really saying not 'this is what happened in every run' but 'of those runs where something made it to the detector, this is what happened'. One can regard the simplified pictures as showing what is understood to have happened for those runs which were singled out by this 'post-selection'. 
A: When I performed this experiment the last time, I used a laser, so no single photons were fired, but an endless stream of photons, so to say. Then, the double slit was so positioned that the maximal intensity way measured at the detection screen (with a photometer).
That some photons hit the area between or outside the slits is very likely, as the laser itself has a certain cross-section. Then, the wave-function would collapse or the photons are reflected and therefore not measured.
In theory, if you perform this experiment with one photon, what would you expect? Well, your wave function should include the possibility of a reflected (or not visible / detected) photon with a non-zero probability. Then, an experiment on it would only make sense with many many measurements, to have a reliable statistic for you probability-distribution, so you end up with doing the experiment many times.
A: If you look up Doctor Quantum on youtube you'll find some (horribly dated) 3D animation videos that DO show the particles that bounce off the space outside the slits. At least initially in the 'marble' demonstration (the first light one also shows illumination on the slit device). They are culled later because of the same reason they've been culled from other examples of the double slit experiment. 
And that reason these particles aren't shown is because they are irrelevant: they don't pass through the slits and so are not part of the "what happens when they pass through the slits" experiment.
Its kind of like asking why people under the age of 18 aren't included in election polling data. Surely these people exist!
A: For multiple particle experiments, I think we could just measure the beam intensities and we would be able to easily deduce that many of the particles are not reaching the detector. The reason we see the pattern still is that there can be such a mind blowing number of particles, that a large enough number of them still reaches the detectors.
It would be even more interesting to setup an experiment with single particles to observe this happening: "hey, I shot a single particle and it did not hit the detector"!
After reading a bit, I think part of the reason why we don't see such a clear experiment easily say, on an YouTube video, is that it is hard to produce single electrons or single photons exactly when we want it, for the most part experiments just seem to reduce the rate of particle production to be small enough such that it is very likely that only a single particle is being produced at a time.
I think one possible approach would be to use spontaneous parametric down conversion as mentioned at Video recording true single-photon double-slit interference by Aspden and Padgetta (2016) to detect this. In that phenomena, two photons are always generated together, and so we might be able to use the second photon in a separate detector without the slit to notice "aha, a photon was sent to the slit but it didn't go through". https://youtu.be/1MaOqvnkBxk?t=130 also suggests that this should be possible.
I've also learnt that "double slit experiments" are for the most part done with biprisms. Or by an analogous "electron biprisms" (a thin wire) as shown at https://youtu.be/zc-iyjpzzGQ?t=340 about the 1974 single electron diffraction experiment by Merli, Missiroli, Pozzi. A true double slit experiment was apparently only done for the first time in 2012 by Stefano Frabboni et al. according to Wikipedia using nanofabricated slits (about 100 nm wide). So the experiment design might also affect if and how many particles are being deflected away from the detector.
A: Here is a double slit  experiment one electron at a time hitting the screen:

The quantum mechanical  setup is : "electron of given momentum scattering on two slits a fixed distance apart , a fixed width". The screen shows the electrons which go through.
The quantum mechanical solution, i.e. the wavefunction $Ψ$ whose  $Ψ^*Ψ$ gives the final probability distribution shown in the last frame, gives the probability for the electron to go through the "barrier of two slits" and hit the screen.
Though the distance between slits is small, if one could place a detector there, or a photo-luminescent  material, there will be a probability of detecting the electrons having a probability to  hit there. One does not need to confirm this, as the wave nature of the probability is evident in the interference pattern.

But the illustrations of particles kind of don't make sense to me. Is it because they are just simplified illustrations?

It should be clear from the above  then, that the electrons are not classical particles, and should not  be extrapolated on a two dimensional graph as particles, except as an approximation over large distances where they do not interact. 
