since you say the character or the people is a biological being, what about the people excrement or organic waste? people use it for coal/charcoal alternative, though i dont know is it compatible with your machine, but you mention coal, so i think it wont be much different. ignoring how your people survive without plant and animal, i just simply assume they has enough food stock/ration or do cannibalism to survive somehow.
from:https://en.wikipedia.org/wiki/Dry_dung_fuel#Human_feces
Human feces
Human feces can in principle also be dried and used as a fuel source if they are collected in a type of dry toilet, for example an incinerating toilet. Since 2011, the Bill & Melinda Gates Foundation is supporting the development of such toilets as part of their "Reinvent the Toilet Challenge" to promote safer, more effective ways to treat human excreta.[3] The omni-processor is another example of using human feces contained in fecal sludge or sewage sludge as a fuel source.
from:https://qz.com/1049248/poop-is-becoming-a-new-fuel-source/
Poop is becoming a new fuel source
Surprisingly, this idea doesn’t stink.
A Kenyan company is taking the excess fecal waste from residents in Nakuru and transforming it into a usable fuel source for cooking and heating.
Truck loads of feces are transported into the Nakuru Water and Sanitation Services Company’s processing plant, where they are emptied into vats and dried for two to three weeks. The dried chunks are heated in a kiln at high temperatures to burn off any harmful gases and increase the amount of carbon, making the feces more flammable. This step also makes the feces powder odorless.
After the material leaves the kiln, it is ground into a fine mixture and combined with molasses in a rotating drum to make briquettes, which look like round lumps of coal. These briquettes are sold for 50 US cents per kilo. Customers say that the fuel burns longer and with less smoke than charcoal and firewood.
Since only one out of every four people in Nakuru has access to the town’s sewage system, the briquettes could be an innovative solution to a big sanitation issue. Excess waste is dumped into rivers and poorer areas, creating health hazards. Although the current capacity for the waste-to-fuel processing plant is about two tons per month, the company aims to quintuple that amount by the end of 2017, reducing the amount of dumped sewage in the local area.