Free: Contests & Raffles.
I would go get my hunting buddy and let him/her finish it off, IF they wanted it.
Might depend on the responding wildlife agent but I went to pick my kid up at my parents several years back in May or June, know it was somewhere around that time because I had to get him to a baseball game and defnitely wasn't deer season. Anyhow, I pulled into the driveway and saw a doe that had impaled herself on my parents fence. The post was through the flank coming out near the tail. She had tried to get loose for awhile it looked like and was very torn up. I shot her on the spot without even thinking about it. I got a little nervous after I had time to think about it so I called WDFW and an agent came out. I left for the game but he talked to my parents and he was fine with what I did, didn't say anything about needing to call them first, just took her away.I doubt I would shoot a limping cow, in fact I have seen a quite a few limping cows but a cow in a similiar situation as that doe, yep.
What if you shoot it and at about the same time your buddy with the cow tag shoots a cow. Then you'd be screwed. It's sad, but I'd have to let it limp away.
Down in this neck of the woods, shooting all the limping cows would fill quite a few tags a day with the hoof rot.