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Background

I am working on a Role Play Video game, and I have a particular island called Morogar in my medieval fantasy. (Magic and Mythical Beasts run wild). Originally an island with forests and a town, the dormant volcano started spewing lava and ash, making the island otherwise uninhabitable. However, many of the trees still stand, albeit dead. The forest was only meters away from the base of this 100 meter tall volcano, but the eruption was relatively small.

Question

How could these trees still be standing? In a normal case, a volcano would wipe out trees. However, I would like the trees to stay.

As of today, about 170 trees are still alive after the atomic bombing in Hiroshima and Nagasaki, they are called Hibakujumoku.

The heat emitted by the explosion in Hiroshima within the first three seconds at a distance of three kilometers from the hypocenter was about 40 times greater than that from the Sun. [...] According to Hiroshima and Nagasaki: The Physical, Medical, and Social Effects of the Atomic Bombings, plants suffered damage only in the portions exposed above ground, while portions underground were not directly damaged.

The following part is translated from the Italian version of the same source:

The survival and regeneration ability of plants, in particular the ability to survive fires, which is greater than the ability displayed by animals, is related to the modular structure of plants, which distributes on their entire body the functions which in animals are concentrated in particular organs. This structure evolved in time as a necessity to survive catastrophe and also predators.

Some of the above consideration on why a tree can survive an atomic explosion also apply to the volcanic eruption.

For the trees exposed to the atomic bomb, they sprouted on the side not directly exposed to the explosion, or in some cases the roots were protected by the terrain and thus remained vital.

Some of the distinctive features of a volcanic blast are also directional and can leave an unexposed side. Think of the pyroclastic flow or the radiating heat from a mass of flowing lava.

The lava and pyroclastic flows are pretty directional, traveling down the path of least resistance. Trees and pretty much anything is going to go up in smoke. And, the rest of the mountain will be not burnt, so trees might still be alive.

I think that depends if the eruption blew the top or side of the mountain off, then you'll have massive amounts of dust and rock raining down all over the area. Those might kill trees but not ignite them since the dust has time to cool as it settles down to earth. Hot ash adds to the force of the uplift by heating the air, so it gets carried up very high. It's only after everything is relatively cooler that it starts to come down -- ash that is.

Heavy material rock, pebbles, dirt will come down immediately and can be hot enough to ignite fires. If the trees are strong and healthy, and there isn't a build up dead wood, limbs, etc, any fire that starts will burn off the ground cover and might not kill the trees. The dust will coat the leaves and the heat can kill them off. But, any trees that have enough energy stored in their root ball will be able to try and regrow leaves next season.

The initial shock wave can cause soil liquefaction which can result in trees momentarily having roots in effectively liquid and they can fall over

Cork is a natural flame retardant, and makes trees able to survive fires normally. in a volcano scenario a pyroclastic cloud would have enough force to simple break the trees, though the flow in a relatively narrow channel. The lava would also eventually burn through the cork, well before it cooled down, but again it tends to flow in relatively narrow channels.

So most of the debris seen around volcanoes are ash and ruble thown out at the explosion, that shouldn't be hot enough to burn through the cork layer.

Maybe not quite what you're looking for, but interesting non-the-less.

Why not consider something which, rather than "survives" the volcano, thrives in the environment you're describing?

The Eucalyptus is well known for needing heat and smoke to germinate:

Most eucalypt species — there are more than 600 in Australia, between 30 and 40 in Tasmania — have evolved traits that allow them to survive and prosper in the fires that will clear that undergrowth.

Some, like the mighty, 100-metre-tall Eucalyptus regnans — also known as the mountain ash, stringy gum or Tasmanian oak — hold their seeds inside small, hard capsules; a fire will instantly trigger a massive drop of seeds to the newly fertilised ground.

The myriad bright green buds that sprout spectacularly from the trunks of other eucalypts in the aftermath of a big fire are another kind of regeneration mechanism, bursting through the scorched and blackened bark within weeks of a blaze.

Within five or six years, ‘a burned forest will be looking pretty good’, Kirkpatrick says. ‘And a large proportion of Tasmania’s flora fits into this fire ecology. Pea plants, wattles — their germination is stimulated by heat and smoke. Fire is really, really important in Tasmania.’

source

Most volcanoes are not going to completely cover their surrounding area in lava. If it works for your setting it would be rather expected that the lava flow itself killed, and mostly destroyed, trees in one area but could leave them standing but dead in another part of the island that wasn't directly impacted by the lava flow. One way to explain those dead trees would be CO2 released into the ground by the valcano, see Mammoth Mountain, CA for an example of this. A second way would be long term ash in the sky blocking a portion on the sun light which could eventually lead to tree death. Some of it is time dependent too, how quickly you need to go from normal island to island of dead trees will change what options are viable.

Would you accept a petrified standing tree. It would still be dead and tree shaped. Perhaps there is a mechanic where by the ash and maybe a follow on rain cloud would create a mud that would petrify the tree. Then over the course of time, this sediment would be washed or blown away leaving the petrified trees still standing. More of a geology answer instead of biology, sorry.

If there were significant structures around to divert lava flow, then the only destructive force (aside from hot air) would be explosions from the volcano. If you posit an uneven landscape, then these pressure waves could reflect and interfere, leading to a "null" where the trees survived or at least weren't knocked down.