Have a customer I'm trying to bid sight unseen. (Scott, this is the TWP 500 person). He said his posts were wrapped in something. I have never seen a post wrapped in a veneer like this. Anyone? Trying to see if it will take a penetrating oil.

Never seen that before. I think it will take an oil just fine. I stained my interior bar with a stain it was oak veneer. Penetrates just fine.

That looks like pine. Customer may be thinking of the below ground wrap for water protection. May be what we see in the pic- the paper showing above ground.
I've seen pine naturally create a thin layer of loose grain skin over old knots and it looks like what I see in that pic. Let us know what you find out.

What you're seeing is a resin pocket or "pitch pocket" that was exposed by the milling process. It probably will not stain like the rest of the 4x4.

Are you going to fill that gap before you stain? Looks to me like the interior is highly porous and will soak up way more stain than the veneer.
Although my business is mainly carpet repair, carpet repair I do enjoy wood deck restoration as a way to work outdoors once in awhile.