The bump out is for a gas fireplace, directly above this is a stone hearth. The 2x10 (3) carrying beam has about a 5’ overhang from the lally column to the end. The end stops under the rim joist location of the main footprint.
I would think it would need support just like the other end terminating in the foundation at the beam pocket, but it pretty much is just holding up the floor.
My guess is that someone did the structural calculations for such a cantilever…or at least, that is my hope. It isn’t impossible, but we don’t know enough about the full actual conditions to verify it. You could say something like: “The cantilevered beam in the basement is unusual for residential construction, and its adequacy should be verified by either researching plans on file in the building department, or by a qualified design professional.”
Richard gave some good advice, but keep in mind that support beams are allowed to cantilever w/out a support post. The distance it spans all depends on the size and type of wood being used for the beam in question.