As John said, different speaker construction requires different cabinets. In all cases, unenclosed speakers are likely to have little bass response. The low frequencies just go around to the back of the cone & end up canceling output.
Small sealed enclosures work well with long throw speakers, however the box volume is determined by the speaker specifications. The volume limits the movement of the cone, preventing it from exceeding the mechanical limits of its design. The cost of the small box is poor efficiency.
Ported enclosures such at the bass reflex can be tuned so the rear pressure from the cone reinforces the front output. The most efficient enclosure is the horn, but it becomes unwieldy when designed for low frequencies.
With the small space you have in your situation, I suspect you will get better results with a long throw designed speaker, at least for low frequencies. The volume & seal of the back side is important to match the speaker design to limit the over movement & damage of the cone.
