how to stop the month acumulation in the sidebar

I’ve setup a wordpress blog for a family member and in the sidebar there is the standard grouping of articles by month.
This is of course all very nice but this particular blog is about a 7 month trip and thus will have an end.

I was wondering if there is a proper way to close a blog? I think that when they get home after 7 months there will come a time that there will no articles be added and no comments should be added so these options should all be closed.

As far as i can see eventhough when I close all comment options and there will be no new articles added, have to figure out how to do all this though. But eventhough I guess the months will continue to be added ? or is there an option to show no months when there is nothing posted in that particular month? or am I expecting wrong and is this the default behaviour anyway?

Anybody got any good tips how to finaly close a blog yet still keeping it online?