19 October sees the 25th anniversary of 'Black Monday'. A lot of money was made (and lost) around that time - a look through the Market Wizards interviews shows how some of the best traders out there coped with an event, the likes of which had not been seen since 1929. These days there are 'circuit breakers' where trading is halted to prevent such a fall.
In my own trading career I have only had to deal with one such day (in October 2008) where trading was halted. This was when the downtrend at that time was in full swing and I was 100% short in my positions.
On the basis that a picture speaks more than a thousand words, below are the charts for the Dow and the FTSE from mid-late 1987, and (as expected) you can see how a trend following system coped well both with the uptrend earlier in that year, and the subesquent sharp drop. Note that the Dow actually gave a short signal on the Dow a week before Black Monday. In the case of the FTSE, the chart is a bit more 'gappy', but you got a long exit signal well before on 12 October, and a short signal (albeit with a bit of a gap down) on the Friday immediatedly prior to the crash.
It should also be remembered also that trend followers did get caught out the day AFTER Black Monday, when Eurodollars rose dramatically following US Government intervention, to prices not seen in months, along with other adverse moves against the trend in markets like gold and silver. Reading Curtis Faith's Way of the Turtle recalls how, overnight, his profits for the YEAR vanished, due to the huge gap up in these particular markets through their stop levels.