Do cancer patients keep burping when they are about to die?

It would depend.: The type of cancer would determine if a patient could have this symptom. Expect it in gastrointesinal cancer, like stomach, esophageal, small intestine, and colon cancers. This is a nonspecific finding that would be highly unlikely to mean that death is near. Other symptoms (dysphagia, abdominal discomfort, change in stool) would be more helpful.

Hiccups: Can be an annoying problem for patients at end of life due to tumor or other irritation of the diaphragm. Belching or burping is commonly due to excess acid, and usually easier to deal with. I'll put in a plug for hospice - they know about and can help manage these problems, as well as others.