left a message stating they were calling on behalf of Yale New Haven Helath.  I believe it is a collection agency.

Yes it is Yale New Haven following up on unpaid bills.  Mine got lost in a pile of paperwork but I did pay it last week,  oops.

ID themselves as Yale New Haven Health, deny they are debt collectors.  But of course that's exactly what they are.  News reports of a few years back show members of this company  owning  a large stake in a New Haven debt collection company.

Yale New Haven Health, see:

https://www.ynhh.org/ynhhs/billing-insurance.aspx

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If they are calling you about a bill, always demand they send you a copy of the bill by US mail.  If they have not already done so.