How to know if someone deleted/quit the shared folder in Dropbox

It appears that the files were not mine to delete after all.

Right clicking on the folder brings up the context menu - the first option of which is Shared Folder Options. Clicking on that option shows the following dialog:

In this case I'm the only member on the list so it's safe to delete the folder. In the other folder there were more names on the list - the person who shared the folder in the first place and others. In this case it would NOT be safe to delete the folder as it would delete it for everyone else as well.

The correct action here is to click on the "Leave folder" option. You get the option to keep the files on your computer and then on OK your usage is reduced by the size of the files that were in the folder.

I had a similar issue, but in my case it was purely a misunderstaning of the Dropbox UI.

When you click the link in the email you get when someone shares a folder with you, there is a "Download" button up at the right on the website you come to (see this screenshot). I thought that button meant that I would download the files once to my local drive – while that is true, it turns out it was also the way to add the folder to your Dropbox.

In case you too missed the function of that button, just click it and select "Add to my Dropbox" (again, see the screenshot).