If you want to view cookies before they are cleared, you can use

Tools > Options > Privacy

If your drop-down doesn't say "Use custom settings for history" go ahead and select that. Then you can access the Show Cookies button.

Sorry, you said without changing settings. There probably are some cookie management add-ons you could use to view your cookies.

Cookies that are removed can't be retrieved. If the tabs were open when Firefox was closed then cookie data may have been saved as part of the session data in sessionstore.js. If you want to keep specific cookies then let all cookies expire if you close Firefox and make allow exception for cookies that that want to keep. You can't use Delete browsing, search and download history on Firefox to clear cookies because that will remove all the cookies that are specified (doesn't obey the allow exception).