Such kind of competition makes a beginner and lousy cuber like me afraid to compete I guess.
In my opinion the situation is not that bad. As far as I know, only the biggest competitions could be like that, which are World Championship, European Championship, US Nationals and now the Asian Championship. Nowadays in these competitions we have to use qualification limits to let only the best competitors to compete, else it wouldn't be possible to organise them even with 3 days. Yes, it is sad for the competitors who are not fast enough for these time limits, but we have to make a cut somewhere. The speedcubing times are decreasing with an amazing amount every year, so we have to face the fact that it is going to be more and more tough to make it to these competitions.
For the actual situation, it depends on how the time schedule goes and what the organisers think. If they decide to stop a solve over the time limit, we have to respect their decision, even if it seems a bad decision.
At Euro we could save a lot of times, so we could let more competitors to do an average, and for example, I didn't stop Lukasz Cicheki during his 14 minutes blindfolded solve, since we had time for that. If we were late with the schedule, obviously I would have stopped him and worst case scenario even make the cut even lower.
Maria, like most of the speedcubers here, I do love you, and trust me, it doesn't matter how fast are you, we love you because of yourself.

Noone wants to scare you off competing, but you need to understand why big competitions are strict. This was the first Asian Championship, which means the organisers might have felt the pressure for making a very good first impression, and from what I have heard, it turned out to be a really great competition.
Of course I wasn't there and don't know every details of this accident, let me know if I'm talking nonsense.
So let's learn from this. When a cutoff time for an event is specified, the "head" judge has two choices.
1) To let the first solve run over the cutoff time and complete.
or
2) To stop the first solve at the cutoff time and call it a DNF.
Whatever the choice, this should be made clear to all competitors before the relevant event. Also, it should be specified on the competition's website so some notice is given (to those that read the competition details). The "head" judge should also have the flexibility to decided 1) or 2) for each event. e.g. 3x3 will be 1) but 7x7 will be 2) etc.
It is not possible to tell that beforehead. How do you know if you will have a delay or not? I still prefer to adjust these to each competition and decide these right there. Once again with the Euro example: If we were more strict and say the time limit is 5 minutes for 2 solves only (we extended that for best of 3 right there), we would have made 3 competitors unhappy for having a DNF and all the competitors less happy for having only 2 solves instead of 3, plus we could have sit there and wait raughly 1 hour for 3x3x3 to start.
Also it is more simple and easier to write this on the website: The competitor should all time respect the main judge's/organiser's decision.