Hedge a corporate bond with a government bond future and you retain credit spread risk. Hedge a specific stock with an index and you retain everything idiosyncratic.
Why it is dangerous. Basis risk is small most of the time, which encourages sizing the position as though the hedge were perfect. It then widens in exactly the stressed conditions where the hedge was supposed to help, because the correlation that made it a hedge weakens under stress.
The pattern - small usually, large when it matters - is what makes it a recurring source of losses.