Quote from AK100:
LTCM didn't blow up so to speak, they got blown up.
Goldmans and others were their prime brokers so knew their positions. When vol started to rise due to the Asian crisis the street smelled blood with LTCM via their positions (remember, they knew what they were).
So Goldmans, as nice people do, put the squeeze on, it's as simple as that, and the rest is history.