If a major fund wanted to sell off enough stock to significantly affect market prices, could they hedge the sale (eg. buy puts) to fix the price to prevent their portfolio from devaluing due to the sale?
A broad based managed fund would be likely to distribute it selling across a variety of stocks, limiting the amount of downward pressure in any particular issue.
There are a number of ways to hedge, each having a different R/R spectrum. This is more in the purview of hedge funds than mutual funds. Put buying isn't that likely because it has a lot of portfolio drag, say 6-8% a year if hedging globally with large index ETF options (DIA, SPY, IWM) and costs even more if there's a sell off because implied volatility expands.
The market makers that "Sell to Open" the puts might hedge their position with sell-side futures or with the sale of highly-leveraged borrowed stock. So ultimately, the buying of long puts is selling pressure on the underlying. Also, there are position limits with options and futures. But the fund could increase its hedging.
It's a known problem that hedging is also selling pressure. Certainly, get into the hedge position before others pile-on.