The usual VC company failure mode is the "zombie". A zombie generates enough cash to cover its operating expenses, but no significant return for investors. It won't die. It demands attention from the VCs on the board for years on end. Too many zombies can choke a VC firm.
The "broken syndicate" thing seems to refer to companies that didn't make it to self-supporting zombie status, are not dead yet, have potential value, and have outgrown the funding resources of the original money source. Kill them off, or find them another funding round? Often this situation involves a "down round", where the early investors lose much of their stake. How often does an eventual success emerge?
I've been involved, as a creditor, not an investor, with one company that went through that - Havok, the game physics engine company. They overexpanded, lost money, found more capital but the founders were replaced, and eventually sold out to Intel. Intel then sold them to Microsoft, where they seem to have be in maintenance mode. So the second round investors came out OK. First round investors, not so much. Creditors got paid because there was never a bankruptcy.
Uber is perhaps the biggest "broken syndicate" company. Despite losing money at an all time record rate, they keep finding new funding sources.