How do we know that galaxies are not losing significant numbers of stars from their outer regions? A major reason for believing in the existence of dark matter is that the stars in the outer regions of galaxies are moving too fast to remain bound to their galaxies, given only the estimated mass of the luminous matter.
But what if many of these stars are not actually bound, and really are in the process of escaping the galaxies?
The loss of stars in the outer portions of galaxies at some stage in their evolution could also be a possible explanation for the "Cosmic Downsizing" mentioned in another recent question.
Given the extremely long periods of rotation, and the comparatively short length of time that we have been observing them, it must be very difficult to determine any rates of change of galactic rotations, so how sure can we be that they have reached any sort of equilibrium?
 A: Astronomers have methods to determine the velocities with which stars and clouds of gas are orbiting the center of a given galaxy, so long as the galaxy presents itself to our telescopes in an orientation which supports those measurements.
Those measurements are sensitive enough to detect any outward (radial) motions as well as orbital (circumferential) motions. The findings are that the outward motions, if present, are small in comparison to the orbital velocities- that is, that the stars in the outer regions of galaxies are not in the process of escaping them.
If one were to posit nonetheless that those stars were in fact in the process of escaping, given the lifetime of a galaxy one would need to furnish some explanation of why at this point in time the galaxy has not already entirely "evaporated" and/or why the evaporation process is kicking in right now.  
A: We observe galaxies at many different distances, and hence ages. While some are rather frayed for various reasons, it is clear that nearby galaxies are not falling apart compared to remote galaxies. 
If stars were actually unbound they would move on the order of a galaxy diameter per rotation period of the galaxy. That would make a Milky Way-like galaxy visibly dissolved in just 250 million years, yet we observe nearby (and our own!) galaxy remaining plus galaxies in the same state billions of years ago. Hence this is not a major process. 
