Based on memory, from what I remember of "A Guide to the Good life" (the book MMM talks about in that article), a Stoic does various things to reduce anxiety (achieve tranquility).
Among other things, the stoic:
1. Engages in negative visualization. This is how you learn to love what you have. Imagine yourself without the things that you currently have, and you will learn to appreciate them more. In modern psychology terms, this is an attempt to reverse hedonic adaptation.
2. Engages in self-denial. The Stoic occaissionaly goes without (such as underdressing for the weather, or walking instead of driving). This enables the Stoic to handle future hardships more easily.
3. Learns to distinguish between the things he can and cannot control, and focuses on those things that he can control. This is fatalism. By focusing only on what you can control, you avoid worrying over those things you cannot control, thereby reducing anxiety.
So, in case someone loses what they have, a Stoic might tell that person to focus his or her energies on those things he can control (like finding somewhere safe and warm to sleep and finding food), and not to dwell on the things they can't, such as lamenting the loss of their possessions, assuming that they are gone forever. Ideally, the Stoic would have already engaged in self-denial, allowing them to realize that they will be able to handle the loss of their possessions.
