@Padma Mody you could have definitely kept the tenant if you had wanted to. You may not have been aware, but all you had to do to was negotiate a reasonably quick timeline with the PHA to make repairs/renovations to fix/replace the HVAC and assure them you would be meeting the letter of the law in proving other accommodations for the tenants during any time where the unit would not be inhabitable due to the work being performed. The tenant would still owe you rent like normal, you would continue to receive the other portion of rent like normal, and the work would be completed.
While a bit over the top, I don't think you should take the police being called too personally. You didn't have a right to enter the unit without proper notice as there was no obvious emergency, and someone trying the door handle definitely would freak me out if I were a tenant inside. Protect yourself and post proper notice that you'll be entering the unit at X time on X date and they won't be able to complain at all. Remember, even if they're past the point of PHA payments ending, they're still residents of the unit until they leave, meaning they have legal rights until they leave or are evicted. Those vary state to state, so consult your local legal resources, but just because its Jan. 2nd doesn't mean you can bust in with no notice.
Finally, you do have the option to work out an agreement with the tenant for them to stay, off the program, for an agreed period of time or until they find a place. IMHO, this would have seemed like the humane thing to do considering they didn't seem to have all that much time to locate and secure a new rental (which can be difficult for even the best tenants with a voucher). The PHA just notified you that they would stop paying you as of Dec. 31 because you were not providing a unit with the minimum level of services under your agreement with them, not that the tenant was evicted. Because of this, I would also check with your legal resources to make sure that you didn't need to post appropriate notice for them to leave, I suspect you did. Remember, the tenant signs a lease with you (or the previous owner), even when they have a voucher. Even when the voucher lapses, the voucher payments to the landlord are suspended/cancelled, etc, the lease itself is still in effect. It doesn't just magically disappear.
Please don't take any of the criticism here personally, the folks here are (usually) critical of folks in an honest attempt to help people succeed in their investments. In this case, it seems that you didn't totally understand how the voucher program or how rights of entry worked and it potentially placed you in a stickier situation than was necessary. We don't want to see you get burned because of it. Much the opposite, we'd love to see you make the best of a busted HVAC system and succeed so you can share your story the next time someone here is in a similar situation!
PS Not a lawyer, consult your legal resources for local law stuff, yadda, yadda, yadda...