Also, even if the previous owner only owed 60k, you have to take into consideration the cost of foreclosing and the lost income if they hadn't been paying for months or years, not to mention any other costs of satisfying tax liens or maintenance issues that need to be resolved before sale.So, speaking as someone who has bought only 3 foreclosed properties:  You make an offer that works for you, and depending on how anxious they are to sell it, and how much interest they've had, they will accept or reject.  

The agent tells me the seller is motivated to sell the property and had no idea the condition it is in (he's out of state), but after two weeks of submitting the new offer the seller has neither accepted nor rejected our new offer.

when my property insurance company suddenly outright rejected coverage because of knob-and-tube wiring and multiple layers of roofing and deteriorated chimney.  

If After submitting a complete offer package and it gets rejected, you should request a copy of the offer signed by the seller declining it.  

Even if you were under contract already, which you weren't, if another higher offer came in, the bank would just reject your offer and start negotiating with the higher offer.

In 99.9% of the cases the party making the offer will be asked to provide the documentary proof mentioned previously, and of course rejected should the seller not believe he will be able to complete the transaction.  

If this guy gets rejected I have no idea what we'll do.

If your not getting rejected 90%+ of the time on your offers then your either not making enough offers or their too high. 

reject...).

My offer on a REO was rejected as too low - the issue with the townhouse is listed at (1)"system did not hold pressure due to damages, unable to find source of allleaks, water heater damaged at side where TPR valve damaged" and (2) "Water Supply and Sewage system was inspected for presence of obvious visible defects.