Cap-weighted index funds do not have to rebalance when a stock falls (this is the most common type as I understand it). Consider a cap-weighted index where there are only two stocks, A and B. At time 0 the have an equal market cap of $1B each. The underlying mutual fund has $20M of AUM, so they hold $10M of A and $10M of B.

    State of the world
    ------------------

    Market caps   A=$1B B=$1B
    Fund holdings A=$10M B=$10M

Now at time 1 some bad news about B is made public. B's price falls by 50%.

    Market caps   A=$1B B=$0.5B
    Fund holdings A=$10M B=$5M

As you can see, the market cap weighted target for B dropped from 50% to 33%. But the fund's holdings of B also dropped from 50% to 33%. No rebalancing is required because the asset price changed at the same time as the market cap weighted fraction changed.

The only time a fund needs to rebalance is when a security is removed from or added to the underlying index. I don't know how that is handled, but I suspect it is predictable and priced in.