Yes, it's about 80%.
There are many illnesses that are associated with suicide. For example, it's estimated that about 50% of people with schizophrenia will attempt suicide at some point in their life, and 10% will actually succeed and eventually die by suicide. So the numbers are very high, and it's not necessarily just people who have depression.
Now, what you're talking about, I think, is the person who has faced an overwhelming stress and has been totally healthy his or her entire life prior to that. Very often those people can be suffering from what we call an “adjustment disorder”. So, someone has a catastrophic reaction to a bad event and can be suicidal based on that.
There are resources in the community that do help with that. For example, local mental health care clinics are designed to address those types of scenario. So, there are resources available, too, for those people who don't necessarily have a chronic illness.