Does any language besides Esperanto have conditional participles?
Esperanto has these only "unofficially"; they're not considered correct Esperanto usage by authorities, but common sense will tell you that they're perfectly inevitable given other aspects of the language.
- skribanta homo = a person who is writing (present active participle of skribi)
- skribinta homo = a person who has written (past active participle)
- skribonta homo = a person who will write (future active participle)
- skribata letero = a letter that is being written (present passive participle)
- skribita letero = a letter that has been written (past passive participle)
- skribota letero = a letter to be written (future passive participle)
- skributa letero = a letter that would be written (if things were different) (conditional passive participle)
- skribunta homo = a person who would write (if things were different)
I once heard someone speaking of a hypothetical situation say "Viaj savuntoj ne povus atingi vin." (Your would-be rescuers would not be able to reach you.) A noun-form of a conditional active participle of the verb savi.)
(It's been sarcastically suggested that the book called "Plena Ilustrita Vortaro" (complete illustrated dictionary) ought to be called "Plena Ilustruta Vortaro".)