Consider a language which has fusional marking for number and something else. A familiar situation is of course case, but we could also consider, say, definiteness or something else. I will, for easiness' sake, use case for the example given below.
Now, consider nouns that are sort of collective by nature - family, team, group, tribe, etc. Case morphology could maybe conflate some cases' number, or even make them behave morphologically quirkily in such a way that, say, oblique cases are marked like plural nouns, but nominative and accusative are marked like singulars (or even, with the potential for distinguishing plurals and singulars in those cases).
Now, we could go on a bit and come up with ways of distinguishing many families/groups/etc from one family/group/etc in the mandatorily plurally marked cases: maybe the number 'one', maybe adjectives have singular congruence for singulars, maybe doubling the plural case marker makes for an explicit plural (but a single plural case marker leaves the grammatical number open), maybe rephrasing so the noun is expressed as a direct object permits for the accusative to distinguish singular vs. plural. One could imagine yet another voice there, one that reduces the emphasis on the object, and simply shifts it to the obliques. This could be an interesting voice!
See, we didn't necessarily turn the oblique into an object by a voice operation, but rather by rephrasing. We might've changed the verb entirely, from, say, 'carry a thing (+ an oblique 'towards X' )' to 'approach X (with a thing)'. Now, what this voice would do - and could be used for even in other contexts where this particular rephrasing is not used to enable distinct number marking - would simply consist of making 'approach a place with a thing' be more about 'a thing' than about 'a place'. Which particular oblique takes on 'object-like significance' is somewhat fluid, and depends on contextual cues - definite nouns are more likely to do so than others, animate nouns more so than others, and maybe some oblique hierarchy like instruments > places > times > ...
Could such a 'voice-like' thing have a participle of its own? Possibly, but that'd be weird.