Beginners fill cells; strong solvers also empty them. Every proven-empty cell tightens the remaining placements, and the technique for proving them is the mirror image of the overlap method: instead of intersecting all possible placements of a run, take their union. Any cell outside the union of every legal placement can never be filled, so it gets a mark (an X in these diagrams).
The cleanest case is a line whose run is already partially placed. Take a width of 7 with the single clue 3 and one known filled cell in the middle. The run must cover that cell, so it can start no earlier than two cells before it and no later than the cell itself. Everything beyond that reach is dead space:
Zero-clue lines are the degenerate case: a clue of 0 means the whole line is empty, and crossing it off is pure profit for every column it touches. Similarly, once all of a line's runs are accounted for, every remaining cell in that line is a simple space — that handoff is covered under punctuating.
Why bother marking, when only filled cells draw the picture? Because empty marks are walls. Techniques like splitting and edge logic run on boundaries, and an X is a boundary you created. A good habit on this site's puzzles: whenever you finish reasoning about a line, spend five extra seconds asking which cells are now out of reach for every remaining run. Mark them before moving on, and the crossing lines get easier while the information is still fresh in your head.