|Cannibal Background Information: Galaxy Evolution|
So between dynamical friction and tidal stripping, what happens to the satellite galaxies? As time goes by, dynamical friction causes the satellites to spiral inwards. As they fall in, they get stripped ever faster. Who wins? Do they reach the center, or are they ripped to shreds on the way? It depends on the structure of the satellite. Satellites which are massive and dense will fall in faster than they are stripped, and make it to the center. Small low density satellites, on the other hand, will get ripped up well before they fall to the center.
Long ago, galaxies may have had many more companions than they currently do. The original companions may have either been absorbed in the center or stripped to pieces. We may be seeing only the remnants of a once-rich population of satellite galaxies.
If many satellites have been eaten by the Milky Way over the course of time, it should be filled with stars which were originally part of satellites but have been stripped out. What happens to these stars? Not much -- they continue to orbit on their own around the Galaxy, but since their individual masses are small (ie, they're just individual stars), they don't feel any more dynamical friction. So they keep orbiting in long coherent tidal streams (like strands of spaghetti), and may actually, as a whole, make up the faint luminous halo of our galaxies and others.