.), we thought it might be best to consider an outright purchase of the entire property.   

Depending on the city where your condo is located, I would consider an AirBnB rental.

PS  Once you get enough documented rental income, if you don't have enough cash for a downpayment, consider an FHA loan (3.5% down, can do 1-4 units).  

How do I find out who’s on that trust and see if they’d consider an offer on the house?

That being said, if you're buying the lien, then you'll need to actually foreclose on the property based on that lien, after which you should consider an eviction, or a cash-for-keys option, as suggested above. 

If the seller would consider an offer of 616k or less I would have no out of pocket?

You might want to consider an Air BnB strategy.

You might also want to consider an FHA 203k loan if you're going to be living there, I've done a few myself and for others :) I trust you will find what works best for YOU!

Let them know this number is for urgent repairs or emergencies only and give them an idea of what you consider an emergency.

And if he MIGHT consider an offer.