I've seen this advice repeated on a couple of websites, e.g. Mayo Clinic:
Asking about suicidal thoughts or feelings won't push someone into doing something self-destructive. In fact, offering an opportunity to talk about feelings may reduce the risk of acting on suicidal feelings.
Is there empirical evidence behind it?
There does appear to be evidence that raising the subject in certain situations can have a beneficial impact.
http://www.bbc.com/future/story/20140112-is-it-bad-to-talk-about-suicide
In an attempt to work out once and for all whether discussing suicidal feelings could make people feel more suicidal, clinical epidemiologist Madelyn Gould conducted her own randomised controlled trial in 2005. More than two thousand students at six high schools were given questionnaires to measure their mood and levels of distress. Half of them were also asked questions about suicidal feelings, which they could answer on a scale ranging from “I never had this thought” to “This thought was in my mind almost every day”. Two days later, both groups were again given questionnaires to assess their levels of depression and distress, but this time both groups were asked about suicidal thoughts. If discussing suicide is harmful then the group asked about suicidal thoughts first time around would show higher levels of distress two days later. But, in fact, they showed slightly less distress than the other group, possibly because they felt their feelings had been taken seriously.
As this article goes on to caution, not every exposure to the concept of suicide has these positive effects.
After a British hospital drama featured a man taking an overdose, and included details of the exact drug and amount that he took, data collected from 49 accident and emergency departments the following week showed a 17% increase in overdoses. In the four weeks following the suicide of a celebrity in Taiwan, where the method used had received a great deal of media coverage, once again suicide attempts rose. Within psychology this is referred to as modelling, where people copy a behaviour they see someone else doing. Many media organisations now follow guidelines to avoid detailing methods.
