What happens to a tadpole's tail as it becomes a frog?

It is absorbed. Cells in the tail are instructed to destroy themselves in an orderly way - programmed cell death, the same process that removes the webbing between a human embryo's fingers - and the material is broken down and reused to build the emerging frog. Nothing is discarded, which matters because a metamorphosing tadpole has stopped feeding.

The whole change is driven by thyroid hormone, and it is one of the cleanest demonstrations in biology: add the hormone to a tadpole's water and it will metamorphose early and undersized; block it and the tadpole simply never grows up, continuing to swim and grow as a permanent larva.

That is exactly what the axolotl does naturally, having lost the response - a salamander that stays larval for life and breeds in that form. And the wholesale rebuild is why amphibians are such sensitive indicators of pollution: a chemical that disrupts thyroid signalling at the wrong moment leaves an animal that cannot complete the transformation, which is why frogs tend to be the first thing to go wrong in a contaminated pond.