When I was an ACO in the 1990s, there were occasions when there were dogs we could not catch.

We had a large cage trap. Some dogs only took a day or two to trap, others took weeks and others were never trapped.

You want a very palatable food, usually canned. Have a dish of water and a blanket is not a bad idea.

If the dog is really skittish, you may want to propp the door
open for a couple of days so the dog adjusts to the trap as any noise or movement may spook them. Once the dog is comfortable eating in the trap, set the trap so the door will close.

Good luck, not every dog can be trapped.