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.