If you are thinking about making a cash offer, we would strongly recommend that you add a contingency to the Purchase and Sale Agreement that states "the property must appraise at or above the sale price" to protect you as the buyer in case the property is over-priced in today's declining market. If the property does not appraise, then you as a buyer may decide to buy or not to buy the property. If this contingency is not allowed, you may wish to have the property appraised before you actually make an offer to purchase. Then you will have a better idea about what price to offer and feel more comfortable that you have made a good decision.
When bank tighten the lending, coop may get hit first, so this unit may have been listing for sale and sold to some buyer who need to do mortgage but could not find a bank willing to lend. Since coop's primary mortgage is really like a 2nd mortgage to the bank because the coop building has a common mortgage already.
This also says it could be your great opportunities. e.g. if you can afford $500,000 cash, those your competitiors with only $100,000 cash may have to move to buy condos or move to buy at NJ, and since you may have fewer competitors, you may be able to negotiate with a better price.
Pre appraisal is good but that may not give you the right market price, keep in mind, market price is set by the buyer and seller, no one else. It could have been set by the seller and many buyers, but since seller put the "all cash deal" to EXCLUDE many of your competitors, you will have MORE power on setting the new market price.
As a rule of thumb, for situation like this, you may be able to get a great deal. Normally, a great deal came from sellers like this setting up some criteria to exclude many potential buyers.