‘Be left to’

In this respect the status of the museums sector as a matter of ‘low’ politics – ‘those residual matters which in normal circumstances could be left to governments and interests in the periphery’ (Bulpitt 1983: 3) – provides the means by which actors internal to the sector can stake a claim to effective policy control and autonomy.

residual matters could be left to governments in the periphery -> what does that mean?!

it seems like it has nothing to do with either a previous sentence or its next sentence.

could you help me understand?!