Do any particles in AGN jets escape the galaxy?
Yes, definitely.
While some matter returns to the galaxy as a so-called &quot;galactic fountain&quot; (e.g. Biernacki &amp; Teyssier 2018), some material is ejected at super-escape velocity, becoming part of the intergalactic medium.
This is one of the mechanisms responsible for polluting the intergalactic medium (IGM) with metal-rich gas (i.e. elements heavier than helium). A recent observation of this is presented by Fujimoto et al. (2020).
The IGM itself is too dilute to form stars, and hence metals, itself, but is nevertheless observed to contain quite a lot of metals, usually seen as absorption lines in the spectra of background quasars (e.g. Songaila &amp; Cowie 1996; Aguirre et al. 2008). These must be blown out from the galaxies, either by stellar feedback (through radiation pressure, cosmic rays, and supernova feedback), or by AGN activity (see also Germain et al. 2009).
Note however that although material can reach relativistic velocities, &quot;pushed away at the speed of light&quot; is just a tad too fast. Only massless particles can travel at the speed of light, but if you're massless it isn't really a big achievement — photons do that all the time, which is why we see the galaxies in the first place.