With some people who are mentally ill, life, in itself, isn’t really worth living. What makes life worth living is the good things in that person’s life (generally relationships). When these things are taken away life is no longer worth living and suicidal thoughts and actions might take place. When someone with a mental illness threatens to kill them self if you leave them you can take it as a back handed compliment. They are living for you! It might not be healthy or right but it’s true.
The experience of being mentally ill (particularly with regards to the elements within your life making it worth living as opposed to life being worth living in and of itself) is a singularity. It’s like those video games where you can reverse the whole gravity of a world and all the elements move in the opposite direction as they were before. Relationships mean a lot to you but they mean so much more to us. Our internal monologue is a cesspit—being alone is more like death to us. What other people say may be bad but it generally isn’t much worse than what we are already saying to ourselves. On a more practical note, relationships counter the self-absorption/rejection vicious cycle which is no good for anyone. And friends who knew you before your mental illness started/worsened (who have stuck) help you relive a healthier version of yourself through shared memories. Just them being there connects you to a part of yourself that was lost through mental illness.