Two bites at the depreciation apple?

I’ve thoroughly enjoyed your podcasts Mark and Matt!
As mentioned before, I own a rental property in an inherited IRA. I understand that a nonrecourse loan against the rental property may require UBIT which could be offset by depreciation of the rental property. Please let me know if your own hilarious way if I completely messed that up!
Anyway, I was thinking about depreciation of the rental property after distribution and wondered if there is an opportunity for two bites of depreciation for the same property? Once while in the inherited IRA and again once distributed from the inherited IRA. Thoughts?
Thanks!