My DH has done this, although I have to point put that I do trust him completely (you've never met a man who wore his heart on his sleeve as much as my DH, so the workings of his mind are practically transparent!)
In this case, he had a female work colleague, he was "intrigued" by her. He went out with her for drinks. He told me (as I say, he can't keep his mouth shut
).
I got a feeling it wasn't right. Pointed put that there is a line, and that this "friendship" was crossing it. He disagreed, but backed off a bit.
Two months later, she got together with another male, MARRIED work colleague, and he left his wife and children and set up home together!
DH is still friendly with her, but they don't go out much now, as new boyfriend doesn't like it.
Not saying she was a scheming man eater, but I just felt that she was respecting boundaries (like pursuing married men).
Tell your DH you trust him, but he must never lie, that he has stepped across a line here, and you want him to back off.