Even if there's no trading and no price for stocks, if all shares of all publicly owned companies were owned by one big index fund the profits from all those co

Even if there's no trading and no price for stocks, if all shares of all publicly owned companies were owned by one big index fund the profits from all those companies would eventually be, one way or another, channelled and attributed back to the owners, i.e. the index fund itself. That alone would set a price for the index fund itself. The fact that there's a market outside of indexing allows the index funds to buy more stock with the dividends received. With no market the index fund would need to pass the dividends forward to the owners of the fund.