A "buy and hold" passively managed fund would be like an index fund when it comes to buying stocks, but the fund would never sell a stock, say if it's removed from the index. If there's a significant net outflow of money from the fund, the fund would use that as an opportunity to dump stocks that it has in excess of its composition in the index. Until then, it would hold on to the stocks it has.
Selling incurs a transaction cost, and unless one has a reason to believe that the stock is over-valued, why sell it? Since passively-managed funds are built on the premise that the fund manager doesn't have any unique insight into which stocks are over- or under-valued, there's no reason to sell a stock when it's removed from the index. The fund should hold on to what it has, to reduce transaction costs.
What am I missing?
Have there been any empirical studies on whether such a fund has higher returns and/or lower risk?
This idea applies to actively managed funds as well: the fund manager would be free to buy any stock at any time, but not sell, except in response to redemption pressure. Or the fund manager could be given a budget to sell in a given year stocks worth say 1% of the money in the fund.