Is nurturing of dispassion an established practice in buddhism?

A while ago I noticed that dispassion (viraga) toward arising thoughts can give great peace. It wasn't really a artificial dispassion, rather, it came naturally after contemplation. Now I'm wondering if it makes sense to actively nurture such dispassion toward not just thoughts but also emotions - like anxiety due to worries of personal outcome. Is this something that actually exists in buddhism? I only know of advice to just observe and be with emotion as they come and go, and never heard of the idea of having a certain view or stance or attitude toward emotion.