Its hard to guess. Evert time you interpolate an image you wind up with a completely new image. The number of pixels you have for and image changes. Going from a large number to a smaller number usually works better then increasing the number of pixels. Usually and your decreasing the number of pixels so the image fits on a low resolution display. Your basically throwing away detail for you have more then the display can display at once. When you print and do not have a sufficient amount of pixels to print a high resolution print you lack detail so up sample and interpolate the pixels you have a dream up details you lack.
The quality change depends the quality of the original pixels on the output device the size the physical image will be a the delta change in the number of pixels. If you throw away too much detail or make up most of the image detail the image quality is low.
If you start with a 8MP camera portrait of a friend crop their right eye out which will be a small percentage of you 8MP and set the crop to be a 16x20 print at 300 the image will be very soft for you made up most of the output pixels.
On the other side of the coin is you started with a 1GP stitch image of Manhattan crop it to an 20x16 aspect ratio image retaining all the image you can ans set 300DPI you will have a high quality image.
Resampling from 300 ppi to 800 ppi (by cropping or any other method) is indeed causing some quality loss because pixels will need to be added that weren't originally present. On the other hand PS is quite good at it and obviously you did not notice any loss otherwise you would not have continued working on the document.
Downsizing again to 300 ppi is not causing much more harm. Barely noticeable anyway.
Of course it's better to avoid this in the future...
This link may also help you.
(although old school of thoughts are always 72 DPI for web and 300 DPI for printing)
One thing in common through my research in the net is that DPI only affects when you print.
If you down back to 300 DPI, it should affect the image quality if you print.
Do you mind letting us know after you down to 300 DPI and print out?