I don't know much about Seneca, but here are some quotes of his:

"Whatever can happen at any time can happen today."

"Cling tooth and nail to the following rule: not to give in to adversity, never to trust prosperity, and always take full note of fortune's habit of behaving just as she pleases, treating her as if she were actually going to do everything it is in her power to do. Whatever you have been expecting for some time comes as less of a shock."

This sounds like good advice, but is it really, taken literally?

People who, literally, are nearly constantly aware of all the bad things that might with some small probability happen are called obsessive, or paranoid. Taken literally, Seneca's quotes invite you to:

There are people who think this way, often not by their choice, and there are people who act as you would imagine such a person might act, and it seems to be a very unpleasant and unprofitable way to live.

I conclude that Seneca's advice is not good advice, taken literally, and rather should be applied with moderation/in a watered-down sort of way.

P.S. another Seneca quote that I disagree with: "It is in no man's power to have whatever he wants; but he has it in his power not to wish for what he hasn't got, and cheerfully make the most of things that do come his way". It seems debatable to me that people are in control of their wishes (desires) -- it does not seem impossible that some desires are simply unchangable givens. Although i also disagree with the opposite extreme, i.e. i think that at least some desires are changable.