Yes, there are, you just need to invest more effort into development of encounter background.[...]
Is there any other lore about dealing with monsters nonviolently that is particularly interesting? Alternatively, what ways of avoiding combat with monsters have come up in games you've run or played in?
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For example (for the monsters), if an encountered party of creatures has an agenda that goes beyond hunger or defend the territory, they may be keen on avoiding combat in order to pursue that agenda.
Two simple and easy ways to go about are making/using two simple tables, and just roll prior to an otherwise typical protocol:
1. Reaction table. If in doubt, start with the classic one:
2. Agenda/activity table. Here's a link to a really elaborate one: OSE Encounter Activity Tables
Secondly, the players, the PCs, need to be made aware of encounter risks. It's not that you don't want them to fight, it's just that a hero party at the start of encounter delving should be wary of engaging potentially dangerous opponents.
Thirdly, rewards. Talking, negotiating or otherwise circumventing violence should be rewarding for characters. Help a troll, and maybe get a few helpful hints.
Then, it's important to present creatures in a way that is sympathetic or appealing. A starving/wounded mother wolf and her whining puppies, especially if it is a giant wolf, or a winter wolf, will be definitely a threatening encounter for low levels, but will probably inspire people to help.
Finally, sometimes it pays to develop or use background stuff. Ghouls in Kobold's Press Midgard settings have an underground civilization. Hags have stories to tell and families. Vampire princes are politicians and nobles.
That's it. Just don't overdo it

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* Risks of overdeveloping stuff include and are not limited to: GM's burnout, overambitious plots that bore players, not enough things to fight.