Did the live event overrun its schedule slot? Does the length of the recording match the timeslot shown on the EPG? And is the length of the recording what you'd expect?
Press "play" during the programme to bring up the status bar - does the red completely fill the length of the bar? If so, the recording is complete to its scheduled length.
Most live programmes in the EPG prompt you for extending the length of the recording, to allow for this scenario.
The duration of the recording will be for the length of the programme in the EPG, unless you accepted the prompt when setting the recording that's along the lines of "this programme is live and may run on - do you want to extend?" There are options for 15, 30, 60 or 90 minutes from memory.
If the programme runs beyond the scheduled time and you said no to extending, you do run the risk of missing the end.