I work in the oil and gas industry (Gulf of Mexico) and there is a slow down with the decline of oil prices.  

For some reason, the tax appraisal value has been declining by 8% consistently over the last 5 years.  

Is the trend in the area declining?

We are VERY early in our process, as I was informed of this whole situation about an hour ago and have been scouring the internet since just gathering all my peanuts to see what we really have here.Based on a quick zillow comp, and my knowledge of the particular area, I am definitely leaning towards the current owner being upside down to the tune of maybe 10-20K as the area has declined a bit more since the 2008 purchase.

It will burst, but because the reasons David Thompson mentions, I believe it will more so level off, rather than a decline like in previous cycles. - David you refer to C class multifamily, which in my opinion, is the safest investment in the DFW market.

(are the growing or declining)

The house has now been up for sale for a year, and is steadily declining in asking price.

It causes some investors to run in the opposite direction and others to kindly decline from "EVER" meeting me in person!

I declined.

I plan on only holding the property 7-10 years (as the IRR begins to decline after year 7).