I've lost cows with 2 month old calves at foot. Put the calf into confinement and adjust it to water. Feed high-quality hay and a high-protein ration. Calf will do just as good or better than it's contemporaries.
I wish I had the housing facilities to feed a bunch of those-type calves (200-250 lbs). Could make a killing on them as they never go for premium dollar.
If you leave the calf to it's own after the cow is gone, he will probably learn to steal milk from other cows as well as drink water. He will usually end up being stunted in this case.