When stocks crash then interest rates go down, which makes bonds go up in value. When stocks crash business conditions are usually bad so investors flee into the relative safety of the bond market, making bonds go up in value. A stock crash may be a deflationary event which drives down interest rates, thus making bonds, with their fixed yield, more attractive, so bond prices may go up if their credit quality is very high.
A basic concept in investing is to keep an allocation of funds in bonds so that when stocks crash you can sell the bonds at a high price and use the cash to buy stocks at a low price.
The effect on bond mutual funds during a stock crash is that some individual bonds may be hard to sell due to their illiquidity, however, the shares of an open end mutual fund that invests in bonds can be redeemed at Net Asset Value from the fund company. Individual bonds suffer from a Broker-Dealer’s Markup-Markdown fees which can be roughly 1% for investors selling less than $100,000 of a bond at a time. It can be even greater percentage for tiny sales. This makes it much easier and less costly to liquidate a bond position by redeeming the shares of a mutual fund when stocks crash.
The concept that bonds go up during a stock crash only applies if the credit quality of the bonds are investment grade, preferably AAA quality. If the bonds are near the lower end of the investment grade rating they may go down in value due to fear that a recession could hurt the issuing company. There are two conflicting forces that affect bond prices during a stock crash: one is the desire for a safe haven from stocks which helps bonds go up; the other force is fear that a low quality bond could go into default during a severe recession and thus its value could go down.
If your goal is to buy bonds as a refugee from stock crashes then you need to get investment grade bonds that have an AA or AAA rating. If you hold A or BBB quality bonds they could go down in value and then gradually recover after the panic subsides. If you hold AA quality they can go down in value during a severe panic. When Lehman went bankrupt that cause a panic selloff of quality bonds with AA ratings making them briefly go down by a small amount. These bonds recovered in a few months. During a severe crash leveraged investors can’t meet margin calls and are forced to sell good assets that they don’t want to sell so bond prices on investment grade bonds may drop even though macroeconomic conditions imply they should go up.