The pipe leading to this exterior faucet was apparently never secured inside the wall (contractor mistake when the wall was built):
So it pulls in and out in use, and no doubt lets rain water drip into the wall.
It certainly means the grade D stucco paper behind has an unintended gap.
Accessing it from inside is hard. What would the external repair options be? What would a proper bracket look like, to secure this pipe from the outside (after caulking the heck out of the gap)?
The right thing seems almost like a floor flange:
But this flange would require pipe cutting, so it could slip over the pipe for solder, and that all seems a bit awkward also, in part because soldering might stress or melt the tar paper inside.
Best Answer
Don't cut the pipe to seek some "creative" or "inventive" complete resolution to a springy pipe. Especially forget about a floor flange. Let the pipe relax to its unstressed position, direct caulk into the space between the pipe and the wall, and push the loose flange flush. If the existing flange interferes with caulking, you could cut it off with tin snips and put on a two part flange. This is not an emergency, you are not getting any significant rain water into the wall around this pipe.
A possible alternative to ordinary caulk would be copper wool. This is used to block openings to prevent rodent entry. Force this into the space around the pipe.
See this How do I secure a copper pipe going through a wall?
This is the only fitting I can find and it does not really look suitable for the outside of a finished wall. https://www.amazon.com/Pasco-5023-Hose-Bibb-Anchor/dp/B005G8UTUC Surely there must be purpose-designed two-part clamps available that would clamp to the copper pipe and then be secured to the wall with screws into anchors.