If you haven't removed the widget from the widget screen, do try that. Press the circle with a plus on the lower left and then the x on the top left corner of all the stock widgets on your dashboard (you can add more than one). If it's still broken when you add it fresh to the dashboard, you'll have to poke it a bit harder.
The widget isn't going to like this - so you'll have to manually clear out the file where the stocks are recorded.
Get ready to log out so save all your work and quit all apps.
Go to the folder below in Finder using this command (or the Go menu) shift+command+G
~/Library/Preferences
Move these two files only to your desktop.
widget-com.apple.widget.stocks.plist
widget-com.apple.widget.stocks.plist.lockfile
Then log out shift+command+Q
When you log back in (or reboot), the widget will make a new container to store your stocks and things should be better. This little dance is called setting aside your preferences (plist files) and starting again with the defaults.
If it works, you can trash the two files on your desktop. If not - you can move them back or not however you prefer. For an app with lots of settings, it's nice to be able to move back the ones you prefer once you've ruled out that file as causing you some pain or other.
Dashboard widget positions are stored in /Users/USERNAME/Library/Preferences/com.apple.dashboard.plist (where USERNAME is your username on your Mac) and can be accessed by using Xcode to edit or possibly even TextEdit. When you open the file, you're looking for the values under 'layer-gadgets' and then 'Item X' (where X is the widget's position number in the Dashboard layout). Just locate and change 'pos-x' and 'pos-y' for your widget.
Good luck!
Best Answer
The Stocks widget gets its data from Yahoo:
The server used seems to be offline though
most probably Yahoo changed the API. I also found pages mentioning that the API got deprecated by Yahoo already years ago. Combining this with the fact that Apple deprecated Dashboard as well you may want to use other ways to access that data.