I think I know what kind of person Z is, there are some people that see the half empty glass, and feel like it is their duty to point it out to everyone else, to help them.
And I think it is alright for this people to provide a friendly warning to their friends and family, but it can be taxing on them. What is happening is that he probably doesn't feel like you understand him, or like you are listening to him. So this causes him to repeat himself in many ways to see if you will "get him".
Regarding warning other people
You just need to tell them that Z cares and tries to help but sometimes is a bit too critical of things, so they should always check for a second opinion, besides Z.
In any case, you hould never go only by one person's opinion when taking a big decision, so by advicing your friends this way you minimize Z' negative impact without really damaging his reputation.
Regarding your relationship with him
Whenever he tells you something netagive about your company, like "it is going to close". Ask him for especific information, like SZCZERZO KŁY, suggested. This way you can keep track of it.
So lets say he tells you:
Your company stocks are doing bad, for this and that
That would actually be useful information that you can check on, and then tell him:
Thank you, I appreciate you showing your corncern for me, I will check
that out
You should ask him for the source of the information too, like it if was from an article or such. Once you have read it, you can tell him your conclusions, something like:
Well it seems maybe their stock went a bit low, but I don't think it
is so bad yet, because they are not doing any budget cuts, and also
stock fluctuation is common, thanks for your information though, and I
will have an eye out for this
The important thing is to make him see you understand the message, paraphrasing Z could go a long ways. Telling him your plan of action too. Or telling him your backup plan. That way he feels he did what he needed to do for you, you have been warned and you understood, then he can drop it.
Afterwards if he continues pressing over this, you just tell him:
Z I really appreciate your concern, but every company can go under
anytime, like you could die any day of your life. I checked the
information you gave me and I will keep an eye on it, but I think it
would be conterproductive to continue stressing over it, if the
company winds up having problems, I think I have time to find a new
job. And thanks to you I now know what I should be paying attention
to. And lets not forget, stress is also bad for our health, so lets
talk about something else.
And you can suggest a topic.
He may get the hint, or continue pressing you. If he does you can decide whether or not you continue trying to explain him that you understood. Or just tell him:
Look Z, i really enjoy talking with you and I would like to talk about
something fun. Dicussing the posibility that one day my company may go
under it is only making me feel bad and making me want to stop. I know
you worry about the posibility of me losing my job, but we already
discussed it and I have a plan in action. And as I said, stress is a real thing
and obsessing about losing my job can cause me health issues. So if we
continue along these lines I will have to pull away from the
conversation.
After that if he insists, just dont answer him anymore unless he talks about something else.
Next time he talks to you about this, you ask him if there is new information, or if it is the same situation he was referring to, if it is the same thing, you tell him that you are aware of it, that things have changed/not changed, whatever applies and tell him that you don't want to discuss it further.
This glass half empty people don't see it as something wrong, they just feel like it is a public duty to tell you. So you just need to tell him that although for him is not stressful to be discussing it all the time, for you it is, and it is also unconfortable because he turns something nice, your job that you like, into something bad.
If he continues with this behavior, as I said you can decide to repeat the technique I said, or just pull away gradually from him. After all you told him you don't like to discuss it, if you don't answer him, he will get the hint.
It is key to tell him cleary that you understand what he said. But just telling him won't be enough, he has to understand it; so use paraphrasing or tell him what you are planing to do and explain him how it makes you feel when he insist so much about it and what is going to happen if he continues insisting.
I have dealt with people like this, sometimes they get the hint, however some of them seem incurable, they just can't understand that you do understand what they are talking about. Paraphrasing them, sometimes helps, but other times there is nothing you can do, they are just that way and don't want to change. So you can pull away from them completely, or each time they start with it just tell him, "look Z, I care about/like/(whatever nice thing you want to say) you, but I am not discussing this anymore". And talk of something else, and ignore anything that he says regarding the topic you already told him you won't discuss.
After that it will be his choice to continue reaching out to you and wanting to be your friend or not. He will eventually learn not to mention it anymore or will shut himself out of the relationship completely, since you won't answer him anything related to this issue.
Just think that probably he is anxious and feels he is doing you a favor, that way I think it gets a bit less annoying. Also he may be projecting fears about leaving his job onto you. If he is unhappy where he is you could encourage him to leave. You only live once, and you cannot be all the time worrying about what may or may not happen.