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There's a lot of contexts where the left sidebar is blank, mainly when
- displaying a node that doesn't belong to a group,
- displaying a view
In the case of (1), perhaps it might work to either theme out the sidebar when it has no content, or an easy filler would be to have a few blocks in there, just recent content like the group node blocks.
In the case of (2), it seems that group views should have the same blocks on them as do group nodes? With non-group views could again either theme out the sidebar when no content, or have recent content block from other content types (i.e. events on announcements / announcements on events).