Or they should be resized to that all columns are visible with possible obscured text in them?
Yes, I think it's better to resize the columns so that all columns fits in the width of the panel.
For instance: It would be nice to have a "Name-column" that uses 60% of the panel width. After that a "Ext-column" that uses 20% followed by a third ("Size-column") that uses 20%. This makes all columns visible even if a user resize DC.
In order to make the implementation easier, it would be nice to have a checkbox (with, for instance, the label: "Adjust columns to window width") that converts the input (which is in pixels I guess) to a relative percentage instead. Of course, the best solution would be to let the user decide for each column, if it should be of fixed width or variable width. But I can only assume it's more difficult and more time consuming to implement.