It’s not impossible, but it’s impractical.
Here’s an advance on technology that isn’t even in commercial existence yet, but may be within a few years:
When you burn fuel with “air” you add a lot of elements that are included in the air into the exhaust gas stream, because “air” is only a bit over 20% oxygen, and the rest is “non oxygen”, including carbon dioxide and water vapor, and about 70% nitrogen. Because of that, a lot of nitrogen oxides (especially) are formed during combustion, and even if we avoid the creation of the nitrogen oxides (which we attempt to do with furnace design and firing temperature ranges), you still have a lot of nitrogen going up the stack. The nitrogen isn’t “bad”, since it was already in the air and no one minded it there, but it means that what’s coming out the stack now is “mostly” nitrogen, making carbon dioxide capture problematic. Then the coal burning itself creates more unwanted byproducts, including sulphur dioxide. The exhaust gases from burning the coal with “air” are many, and mostly unwanted, and all have to be treated differently.
But what if you burned the coal with pure oxygen? You’d have fewer byproducts (still carbon dioxide and particulates, still water vapor and still sulphur dioxide, but no nitrogen and no nitrogen oxides), which would automatically reduce the non-CO2 gas stream. Treat for the sulphur dioxide, flyash and other particulate emissions (a routine, if still fairly expensive, treatment at modern plants) and now you’re left with primarily carbon dioxide and water vapor. If you can find a way to shunt off the water vapor you’re left with carbon dioxide that could theoretically be sequestered and even refined and resold as a commercial product.
The way to do that is… set up another plant immediately adjacent to the coal-burning furnace to extract oxygen from the air, and then pipe that oxygen into the furnace to support the fuel combustion, and recycle all of the waste gases that aren’t carbon dioxide and water vapor back into the furnace. This makes it possible to sequester and store or refine the carbon dioxide (since we don’t have to separate it from the nitrogen oxides, which is prohibitively difficult), and the only thing that’s going up the stack is water vapor.
It’s going to be expensive, because you don’t extract oxygen from air “for free”, and it’s going to be somewhat dangerous, because pure oxygen is highly combustible (and coal dust in air is already explosive, which is one reason to recycle waste gas into the furnace, to ‘cut’ the oxygen), but it’s being done in test furnaces now, and should be showing up commercially within the next ten years or so… as soon as someone wants to be the first to buy that arrangement, and pay the considerably higher cost of power generation for twenty years or more to run that.