They failed because they expected volatility to behave roughly as it had done in the past. The sold high volatility options and bought low volatility options. The events of 1998 caused volatility to blow out to new highs and this was not something their system had allowed for. They did not cover any positions, as they considered the enormous amount of trades as sufficient risk control and diversification. However there are many reasons LTCM failed. One reason was that they got too big for the markets, and in the end there was nobody to take the other side of the trade.
My system is ZERO risk as all positions are covered.