Whether the spread of disease or disaster, sometimes it is difficult if not impossible to contain. In financial terms, contagion is often thought of along the lines of 2011; Greece started it and it spread throughout the rest of Southern Europe. The euro was coming apart, and what "it" was didn't seem to matter.
The eurodollar system is not a single, monolithic whole. It features many different pieces that sometimes don't fit together at all. There is always something wrong somewhere, even during the best of times. It is eerie in hindsight, but there was a huge outbreak of repo fails, for example, in 2001 following September 11th. It kept up for months on end, until the middle of 2002. Outside of dot-com stocks, the system didn't crash.