eslHQ - 'will be being+past participle'

Yes it exists - it's used to make predictions (hence will) about on-going present or future events, and is of course a passive. Compare the following, which might occur in reply to a question like Do you know what they're working on today? :

Statement of factual event (active) : They are printing the leaflets this morning.
Prediction of event (active) : They will be printing the leaflets this morning.

Both of those can be turned into the passive, perhaps in reply to What's happening this morning? :
Statement of factual event (passive) : The leaflets are being printed this morning
Prediction of event (passive) : The leaflets will be being printed this morning.

All that's happening is that the fact is being turned into a prediction by adding will, with the grammatical consequence that the following verb becomes an infinitive.

It's not a common structure (it can sound clumsy and the simple infinitive is often preferred), but certainly exists. Here are some authentic examples from Google :
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