Are corporate bond (funds) related to stocks? (Markets)

I am investing in World Markets ETF’s and some government bond ETFs I try to avoid corporate bond funds as you often hear that they might be more related to the market and stocks. But thinking about that I wonder if that is true. When inventor expectations are low stock prices fall. But that should not necessarily mean that corporations are unable to fulfill their bond coupon payments. I can imagine markets being down, but corporate bonds are still safe. So my question is, is this alleged relati