On the stock markets, every time someone sells a share, someone buys it, or in other words, equal numbers of opposing bets on the future are placed each day. However, in the case of open-end mutual funds, every dollar redeemed in a day isn't necessarily replaced by an invested dollar, and every dollar invested in a day doesn't go to someone redeeming shares. Still, although mutual fund shares are not sold directly by one investor to another investor, the underlying situation is the same as stocks. Similarly, any new investment would require the manager to find someone to sell shares so the new investment can be put to work. A typical mutual fund has some cash to use as a buffer, which confuses the issue but doesn't fundamentally change it.
Some money comes in, and some flows out, much of it cancels each other out.
If there is a small imbalance, it can be covered from the fund's cash position, but not if there is a big imbalance.