Also in the non cannon Star Fleet Battles, about 60% of all Klingon ship crews are non Klingon subject races. They use them as infantry and workers, while the Klingons are officers. That's why the Klingons live in the small part in the front of the ship and the slaves live in the back with the engines and the other problems of living in a Klingon ship. The narrow neck is defended in case of a mutiny and can detach to escape with the officers. Not that it matters, but I like that version.
Technically speaking, the non-Klingon subject species in the Star Fleet Universe are not slaves, though they are considered to be less "politically reliable" than "ethnic" Klingons. The occasional mutiny (or colonial uprising) aside, the vast bulk of Klingon subjects are in fact loyal to the Empire. Indeed, some of the more senior subject planets are enmeshed into the Imperial bureaucracy itself.
For example, the Dunkars (orange-skinned humanoids) are considered to be the most trusted subject species; the King of Dunkaria is simultaneously the Count of the local Klingon province (as shown on the
Federation and Empire hex map; Dunkaria is the major planet in hex 1112). Dunkaria has a more robust economy than Klinshai itself, and pays significant tribute to the Empire. But on the other hand, if the Dunkars were independent, they'd likely have to pay at least as much, if not more, to run their own deep space fleet. Plus, since Dunkaria is close to the border with the
Lyran Star Empire, where the felinoid Lyrans' subject species are confined to their home planets and are typically treated more harshly than those in the Klingon Empire, the Dunkars arguably endure the lesser of two evils. Politically-speaking, the Dunkars are mostly left to run their own affairs, so long as they remain loyal to the Empire.
(There is more data on the Dunkars, and on a number of other Klingon subject species, in the Klingon sourcebooks for the
Prime Directive RPG.)
Actually, one thing that helps explain why the SFU Klingons bother with using subject species on their ships is the Klingons' own history as former subjects of a precursor realm (now known only as the "Old Kings"). The Old Kings showed up in orbit over pre-spaceflight Klinshai (and over Dunkaria and certain other worlds now in Klingon space), offering to recruit the Klingons (and Dunkars and others) into their service. Once the Old Kings decided to abandon the Alpha Octant*, the Klingons used salvaged Old King technology to establish an empire of their own; one in which this kind of "subject race" setup would be re-established, only now with the Klingons themselves being the ones in charge.
That said, going so far as to cross the Klingons is not a good idea. Another former Old King subject species, the Vergarians, made the mistake of launching a fleet-wide rebellion in the early days of the Klingon Empire. In response, the Klingons blasted Vergaria back to the Stone Age and imposed harsh penalties on the survivors for many decades afterward.
Which is why one subject species in particular, the
Vudar (reptilians with a high level of radiation tolerance) are quite careful in how far they push things. Uniquely, the Vudar were allowed to build and operate their own warships, mainly since they were better suited to operate in the hazardous regions of the Empire along the Galactic Rim. Later on, the Vudar established a greater degree of autonomy, but never went so far as to fully break with the Empire (who, in turn, were careful not to push the Vudar to the point of outright rebellion). In fact, the "fiction" of Vudar neutrality had its uses, since it allowed the Vudar to claim three provinces which once belonged to the
Hydran Kingdom (who, like the Lyrans, are on the far side of the Klingon Empire from the Federation) - and allowed a portion of the taxes levied from those provinces to be fed into the Imperial coffers.
*In the SFU, the Milky Way Galaxy is divided into
24 sectors, which are grouped into five habitable regions. The Klingon Empire is mostly in the Gamma Sector, a sub-region of the Alpha Octant.