Glial cells carry out inflammatory/immune responses by acting as pseudo phagocytes in the central nervous system. They also sever unnecessary synaptic connections between neurons during development, as our brains make far more connections than we actually need.
Interestingly enough, you can find a high number of these cells in post mortem tissues taken from people with neurodevelopmental disorders, suggesting that inflammatory cytokines released by glial cells may mediate certain disordered phenotypes.
In my opinion, I think the glial cells that remain after death are cleaning up dead neurons and astrocytes, severing lots of connections in many different neural networks and pathways, thus beginning the final shutdown of the mind.