Future Continuous and Perfect Continuous tenses in Passive Voice
Of course they're possible.
As to whether you'd want to use them, that's another question entirely. Each new auxiliary verb you use further narrows the temporal interpretation of the verb. After a certain point, it just doesn't matter 99% of the time. In other cases, it just sounds weird.
For the perfect continuous, that's likely because of the double be (has been being) that, like had had in pluperfect, even though it may be perfectly justified, often sounds better simplifying it (has been). Depending on the verb you need, you can partially avoid this slight cacophony by using a different auxiliar for the passive, like get, although that doesn't solve the convulatedness.
Continuous with modals will and would work exactly the same:
| It will have been getting written for hours || pres. bare inf. past.part. pres.part. past.part. || mod.fut. aux.perf. aux.cont. aux.pass. main |
Here I have a sentence, with the morphological form written on the second line, and the purpose of the verb (to generate the future, auxiliary to the passive, etc)
Modal will (or alternatively would) accepts any non-defective verb. Have fits the bill, and merely requires a past participle. That's been, which is used to form the continuous and simply requires a present participle. That's getting, which is one of the auxiliaries that can form the passive (you could also use being here). It needs the past participle of transitive verb, and written is just that.
Of course, if you use another structure other than modal will for the future, like going to it's even crazier:
| It is going to have been getting written for hours || pres. pres.part. bare inf. past.part. pres.part. past.part. || aux.cont. aux.fut. aux.perf. aux.cont. aux.pass. main |
I suppose if it's really important to emphasize that the fact that it is currently preparing to be in the process of being marked upon at some point in time prior to some time posterior to now, that works great, but really, it's overkill :-)