That is a fairly common question -- especially in dove season, where fence lines are often the best hunting spots, and wounded birds frequently go down on the neighbor's property.
The answer, too is fairly clear, and may be disappointing:
"No person may pursue a wounded wildlife resource across a property line without the consent of landowner of the property where the wildlife resource has fled. Under the trespass provisions of the Penal Code, a person on a property without the permission of the landowner is subject to arrest."
This information comes directly out of the Texas Parks & Wildlife's Outdoor Annual, Hunting & Fishing Regulations.
So what does this mean? In my mind, it translates to 2 things:
1) never take a shot an an animal unless you know that you can take it down (be realistic about your aim, distances, and firepower); and
2) if you find that tropy buck on the neighbor's property, call the neighbor and ask permission to retrieve it.
If the neighbor cannot be reached, call a Game Warden. Since game waste is also a crime, the Warden is likely to assist you, or at least monitor the situation. remember, RESPECT is an essential element of hunting and of private property rights and the law.