My relative has caregivers who puree food and use a plastic tube and pour it down her throat. Is this appropriate?

No, puree food can be fed with a spoon like a baby. Have you seen this? If so, was it questioned? Need more info.

Who is telling you that this is what is being done?

Are you talking about a feeding tube? Because if you are not then I think that sounds criminal, there is absolutely no way it would be acceptable.