My 90 yr old mom got a huge increase in 1099-DIV “distributed capital gains” and now has a large unexpected tax bill.Can this be avoided, because the fund also drops too?

"the only drop in value will come if you liquidate some shares..." is not true.

It's entirely possible, and not all that uncommon to see large capital gains distributions, in particular, and a drop in the market value of investments.   I imagine this is what you're seeing.  

 The dividends and capital gains distributions (which occur because capital gains were realized within the fund) are income in the year they are declared, even if they are reinvested in the funds.  And even if the market value of those funds decreases (and the funds continue to be held.)

The loss in market value of the funds/shares is not deductible until realized by the shareholder through a liquidation or sale. 

Often, when capital gains distributions are high due to a large sell-off within a mutual fund, there is also a dip in the market value of the fund itself.   Hopefully the amount of the dividends and capital gains distributions is equal to or more than the loss in market value (but if they were reinvested, and the value is still down, then we know that's not the case.) 

It's too late now to sell while the fund is depressed for a loss to offset any of those gains -but that's not an ideal strategy anyway. 

This is never fun, but at its the nature of those types of investments. 

If your mother has a financial advisor - talk to him or her about more tax efficient investments for your mother.  There are plenty out there!