I performed a complete cache clean and discovered that this obliterates everything under /media/ (as noted by me below and later correctly observed by an answer, it is indeed just the cache that is being wiped under the /media/ folder). Unfortunately there are some email distributions from the past that rely on these images and I am curious as to whether there is a way to regenerate all of the thumbnails / cache entries under the /media/ folder?
So, for example, in this situation I am seeing missing files such as:
[Mon Apr 15 11:46:01 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/T/E/TE0213.jpg
[Mon Apr 15 11:46:01 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/F/X/FX0413_1.jpg
[Mon Apr 15 11:46:01 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/F/B/FB0413.jpg
[Mon Apr 15 11:46:01 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/F/K/FK0413.jpg
[Mon Apr 15 11:46:02 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/E/V/EV0413.jpg
[Mon Apr 15 11:46:02 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/F/P/FP0413.jpg
[Mon Apr 15 11:46:02 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/F/E/FEA0413.jpg
[Mon Apr 15 11:46:03 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/F/Z/FZ0413.jpg
[Mon Apr 15 11:46:03 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/G/B/GB0413.jpg
[Mon Apr 15 11:46:03 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/F/S/FS0413.jpg
[Mon Apr 15 11:46:04 2013] [error] [client xxx.xxx.xxx.xxx] File does not exist: /home/username/public_html/domain.tld/media/catalog/product/cache/0/image/265x/4df79eab33525d08d6e5fb8d27136e95/F/U/FU0413.jpg
When I do look for the images, for example, I do see the originals present in:
media/catalog/product/F/U/
The goal, therefore, is to regenerate all of these appropriately.