New answers tagged compression
Lossless cropping of a JPEG image is possible using the "jpegtran" application that comes with libjpeg; see https://en.wikipedia.org/wiki/Libjpeg. With other image-editing software you can minimize the loss by ensuring that the cropped area has dimensions that are multiples of 8 and is located with offsets being some multiple of 8 from the upper lefthand ...
If you are using Photoshop® then I don't believe that the image compresses when it crops. The compression happens when you resave the document as a JPG. It is always best to start with the highest lossless uncompressed image format you can such as .NEF, .BMP... others (?) As the saying goes, poop in poop out.
Top 50 recent answers are included