The index funds will sell out on the close of its last day in...

The index funds will sell out on the close of its last day in the index. You see a massive chunk of turnover at the 4.10pm match in every stock as the index funds rebalance.
Active funds may sell a small number if they care to keep the bet size the same, for example, if TGR was .25% of the index and the funds weight was 1.25% they might sell .25% in that 4.10pm rotation to maintain their overweight at 1.00%.
If they were mandated to only hold index stocks theyd have to sell, but this is extremely rare. Fund managers are never constrained like that, it would bar them from participating in IPOs, for example.