What will happen to black holes when the universe is no longer expanding?
No one actually knows.
Black holes grow in (theoretical) mass by accumulating matter. When the universe stops expanding is also debatable, so if the universe stops expanding, that means that matter is spread so far apart that black holes will no longer consume matter and will simply "stay there".
If the universe stopped expanding the black holes could cause the expansion to reverse and start contracting.
The theories of an oscillating universe postulated that the black hole would grown in size pulling all the matter and energy of the universe back into one massive black hole. The concentration of all the matter and energy in one small place would create another big bang starting the universe over again.
The supernova studies of 1997, 1998 (Supernova Cosmolgy Project, High Z supernova search team , Supernova legacy survey) discovered that the expansion of the universe is increasing. This means that the expansion will not stop or even slow down. The black holes will slowly dissipate as the universe approaches maximum entropy will near zero temperatures, and no useable energy or matter.
The implications of these studies is that the Universe is an open system, and that the matter, energy continuum is not eternal, nor self existent as postulated by most scientific world views. These studies are being challenged and questioned today. However the best present empirical evidence is that the expansion of the universe will not stop.