VCs are expected by their LPs to get 15-25% ownership. So there is no way for an investor to invest $2m on an $8m round and get to that level of ownership.
Worth mentioning that given the current cheap money, a lot of the investment is leveraged, on credit or timed. So you don't have to have 2m sitting idle in a bank to lead a round.
As far as I understand VCs(General Partners) don't hold investment money. They just get paid fees and have a mandate from Limit Partners to invest, so when they want to invest, they just call on LPs to transfer the money.
I imagine each VC fund has a multitude of LPs and they each manage cash based on their own strategies. The key is that they have enough liquid assets to meet the obligations in a timely manner.
Obviously, each fund is set up separately and might have a different structure.
I would guess ~$2m, but you gave the impression that it would be more about $5m.