Q:

Are "I will have been going" and "I would have been going" rarely used today?

As far as I know these are tenses that you do not often use. Am I right?

Will have been + verb+ing
Would have been + verb+ing

A:

You are right that the two constructions are not often used. This is because they express uncommon ideas. Both are grammatical, however, and could be used as follows:

By the time I retire I will have been working here for 45 years.
If you had called me 10 minutes ago, I would have been sleeping.

