there are cases where the bypass ration is between 1 and 2 - sometimes called, at least partly in jest, a "leaky turbojet]
The Rolls Royce Conway engine had [depending on mark number]had a by-pass ratio of between 0.3 and 0.6 and was considered state of the art back then
We were taught that the term by-pass referred to an engine where although the air by-passed the combustion chambers it was retained in ducting within the engine case.
Where fan /compressor air passed along the outside of the powerplant casing then this engine was called a turbo -fan