Crossing Parity

Hard Used by Smart Hint

The loop is closed, so any straight line drawn across the whole board crosses it an even number of times. When every crossing edge in a row or column is decided but one, that last edge is forced — whatever makes the count even.

Edge on the loop
Edge the technique adds
Edge ruled out
Cells that establish the pattern

How it works

The finished loop is one closed shape — so a straight line drawn across the WHOLE board must cross it an even number of times. Zero, two, four… never an odd count.
Look at the middle row here: its four crossing edges are the four vertical edges along it, and a full left-to-right sweep crosses the loop once for each of them that's a line.
Three of the four are already decided — one line, two X's. That's one crossing so far: an odd count.
The last crossing edge must make the total even, so it's forced to be a line. (Had the count already been even, it would be forced to an X instead.)
This works on any full row or column, any time exactly one of its crossing edges is still undecided — no clues needed at all.