How can I inspect disappearing element in a browser?

An alternative method in Chrome:

• Open devTools (F12).
• Select the "Sources" tab.
• While the element you want is displayed, press F8 (or Ctrl+/). This will break script execution and "freeze" the DOM exactly as it is displayed.
• From this point, use Ctrl+Shift+C to select the element.

(This answer only applies to Chrome Developer Tools. See update below.)

Find an element that contains the disappearing element. Right click on the element and apply "Break on... > Subtree Modifications." This will throw a debugger pause before the element disappears, which will allow you to interact with the element in a paused state.

Update Oct 22 2019: with the release of v. 70, it looks like FireFox finally supports this kind of debugging 2 3:

Update Sep 15 2020: Chrome has an "Emulate a focused page" option (you can get it from the [⌘]+[P] Command Menu, or Global Preferences) for this exact need. 5 - h/t @sulco on Twitter