If a person presents themselves via phone as actively suicidal it is important to refer them to the National Suicide hotline as soon as possible:
1-800-273-8255.
The caller may be more comfortable with chatting with the Suicide Prevention Chatline.
The National Suicide Lifeline has the ability to track a call and to track call-back numbers and therefore they are able to track a call get a third party on the line in order to provide emergency services to callers even when they have not named themselves. This is critically important for calls to the helpline.
National Suicide Prevention Hotline Policy for Helping Callers at Imminent Risk of Suicide Manual
This manual is extremely valuable: and not a substitute for immediately referring a suicidal client to the hotline itself.
It is nice to know what to expect when calling a suicide hotline. Here is an article that addresses exactly that: https://www.buzzfeednews.com/article/carolinekee/what-happens-when-you-call-suicide-hotline