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 relation between corporate bonds and stocks real?