Thanks for the replies. I was thinking it was one of those covers, because it looked funny. When I asked the owner about it, this is what she said and I quote:

"I just asked my dad about the dash and he said it is the original dash. No protective coverings. The car was supposedly kept in a garage in Norfolk VA. My dad's uncle is a used car salesman and he found this car for my dad".

Perhaps he thinks it is the original dash. It is not a big deal, but I was wondering about this thing. Do they glue on, or are they easily removed?

This is strange, because this was when I was interested in the car back in January. The owner decided not to sell. The car has recently became available again, or at least I hope it is.

BTW- the car is a 85' 380SE - it has very high miles (over 200K), but it is cheap - around $1,000., but it gauranteed to be in good shape all over, including running conditions.

Thanks again.