Most bigger funds do, but with smaller funds, it’s murkier.
A VC fund of > $100m-$150m or so will typically keep 60%+ of the fund in “reserve”. Some of these reservers are used to double-down on their winners. But some are also used to support the portfolio companies that are doing OK but not great. And in particular, to support their “pro rata” in the next round, even if they don’t really want to do it.
But smaller funds often see their “reserves”, if any, as often 100% discretionary. Only for their winners.
The good news is for signaling, it doesn’t matter that much re: smaller funds and if they don’t participate. No one will care if a $10m fund doesn’t do their pro rata in the next round. They will care if a $500m+ fund doesn’t.
A $70m or $100m fund? That’s where it’s grey. The bigger the brand of the fund, the more important it will be. If no one has heard of the fund, it may not matter at this fund size.
As a rule, bigger funds sort of have to “follow” into the next round.