PSE 2018 Cropping Issue - Destructive vs. Non-Destructive

You need to Flatten the image before Save.

Layer>Flatten

Or if you still have a Background Layer you could use Layer>Merge Visible which has a keyboard shortcut

of Shift+Ctrl+E (windows) or Shift-Cmd-E (mac)

https://forums.adobe.com/people/Jeff+Arola  wrote There is no preference in elements for choosing between delete cropped pixels or not.

That is, in the Elements editor.

It is available with your saving options if you use the ACR (camera raw) plugin, with a lot of advantages.

Using an ACR workflow, even for jpegs, is much faster with better image quality.

- You use the option to 'Open in ACR' from the editor.

- You open a batch of files to save a lot of time applying the same edit to some of the files or only to individual ones.

- The 'crop' tool is non-destructive. You can turn back to the original value or default ones.

- Your crop custom setting (square ratio) is sticky, available for any ulterior session.

- Once you have applied as many edits as you want in the ACR, you have two choices:  clicking 'Done' or 'Open'.

- 'Done' simply writes the sliders and crop setting in the metadata header of the jpeg, not in a sidecar file. The settings are also written in the catalog. The organizer thumbnail is updated and shows the crop. The next time you open the file in the editor or the organizer, it opens in the ACR dialog. If you open your jpeg with a third party browser or editor, the ACR edits will be ignored. After editing a session of say 50 files, a single click on 'Done' is enough, evrything is saved without creating new files nor xmp sidecars.

- 'Open' starts like 'Done' but if you 'select all', it opens the whole batch of edited files in the editor where you can edit with layers and all the usual tools, and save in your preferred format with 'save' or 'save' as.

The ACR crop tool:

To get the options, press the crop icon a few seconds until you are shown the drop-down menu.

To remove a previous crop, click the icon and outside of the former crop.

The organizer and jpegs edited in ACR.

It's a pity there is not an option to open new jpegs in ACR from the organizer. The first time, you have to open the jpegs from the editor, which is very fast if you open a reasonable batch (I do use 20 to 50 files by batch). Once you have clicked 'Done' or 'Open', the next time, the jpegs are automatically opened from the organizer in ACR. The thumbnails are updated.

Batch workflow for files edited in ACR.

From the editor:  'File >> process multiple files'

From the organizer:   Export as new files.

You may take full advantage of the non-destructive editing in ACR by simply using the 'Done' option or the 'Open' one followed by a 'save as' one in version sets in the editor. You organize your pictures into albums or add keywords. In your case, I would use those albums and the options of the 'export as new files' of the organizer to create a temporary folder to send to your partner. No need to keep them after they have been sent, since you can do it again any time later. You'll notice it's very similar to the Lightroom workflow. The difference for me is that I need to open in the editor a small part (5 to 10%) of those files. For those files I do create version sets in psd or jpeg. When exporting as described above, I select the album. I don't care if some are versions or originals with ACR setting (or if they are in different formats like jpeg, psd or tiff:)  they are all exported as I want to the temporary folder.