It all depends on what gets dropped off when you add a new score. Let's say I had an average of 71.7 and my 10th best score is a 40. Also assume that I have four other 40+ scores that are being dropped from the average.
If I go out and shoot 36, it'll cause that last 40 to drop off the board. My average would drop from 71.7 to maybe 71.1 because I'm taking 4 strokes off my 10-round total. A lower total means lower average.
In this case, my average would actually go down further by shooting par.