When mail receive is happening, various activities are not allowed in Claws. One of them is to exit the application. That option is greyed out on the file menu, but not in the trayicon menu. Pressing exit on the trayicon menu at this time does nothing. Ideally, pressing exit should exit, cancelling (or abandoning) any receive if necessary. If that is not practical then non-functional menuitems should be greyed out.
This is still a problem with 3.10.1 windows. File->Exit is grayed out. ctrl-Q starts the quit sequence and launches the queued messages warning dialog, but silently fails. After the first attempt CTRL-Q doesn't seem to do anything. The close box isn't responsive. Workaround Force quit from the process manager works as expected.