If someone accepts a friend request from you, Facebook sends you a notification, both on the service and via e-mail (unless you disable this functionality). If one of your friends deletes (or unfriends) you, Facebook does not notify you. The company says so explicitly in its Facebook Help Center:
If I unfriend someone, will they be notified?
No, but all friend links are reciprocal, so you will be removed as a friend from their friend list as well.
Facebook does this so users don't feel guilty when they unfriend someone. Unfortunately, some users just can't help themselves and are unbearably curious who is unfriending them, and when.
FFChecker keeps track of your Facebook profile in the background and notifies you on a frequent basis who unfriends you. Here's the official description: "Regularly checks your Facebook friends to check whether anyone has removed you from their friends."
You can set how often the plugin should check your friend list (the default is two hours). The time limit is there so that FFChecker isn't constantly working: it only activates when it's time to check. Two hours is way too frequent; setting it to 24 hours or even more should be enough for you.
When FFChecker detects that one or more of your friends have unfriended you, it displays a message informing you of the event. The message also includes a link to ex-friend's profile page.
The extension works because it can compare the list of Facebook friend ids saved in Chrome's cache. If you clear your cache (Wrench menu => Options => Under the Bonnet => Clear browsing data…), the plugin won't work until Chrome caches you Facebook Friend List again.
This Chrome extension is a modified version of the original Greasemonkey script, which is available on Userscripts.org and was developed by the user znerp.