If the consumer is entitled to receive periodic statements, someone must be providing it to them as required. If you were buying a large number of loans with plans to service them, wouldn't you make arrangements to keep the periodic statements going before you made that purchase? I'm not sure how your institutions choice to purchase a loan comes into play here.
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My opinion, take it for what its worth. Opinions expressed are my own and not those of my employer and are not legal advice.