I'm not sure how common this is for other girls but I have had it happen to me unfortunately a lot. My reaction is drastically different if the guy is a regular or someone I know, but in general it's always been strangers to me.
SO I give them a list of hotlines as well as link them to places like 7 Cups of Tea where they can talk for free to someone who's there specifically to listen. I tell them if they feel absolutely hopeless, to go to the hospital. And I tell them I'm sorry, but I'm not equipped or able to help them. Which is true, and honest. Invariably they try to push it, because I believe most of these people (on cam sites, obviously, not suicidal people in general!) are just trying to get attention, and I just repeat that I can't help and I'm sorry they're struggling but here are some resources. I say all of this nicely & try to be supportive without encouraging the dialogue.
It's really, really hard, I think for anyone, to say "sorry, I can't help", and as someone who's both quite empathetic and pursuing a career in helping, it's difficult. But the vast majority of us truly aren't equipped to help, and it is often a power play on the guys behalf to try and control your time or emotionally manipulate you. I wish I wasn't so jaded as to think that, but welcome to the internet I guess, lol. Again this presumes he is a relative stranger to you.
Anyways I think sending along resources is the best thing you can do for his mental health and your own.
(Also if you get a message from him saying he's killed himself and this is his friend/cousin/wife/etc telling you, don't stress out - people do this a lot online and it's cruel and fucked up but likely not true.)