Can cancer drugs cause a kidney to become atrophic and damage the other?

Yes. Certain cancer drugs are known to be toxic to the kidneys, which is why your kidney function is closely monitored on them.
Cancer Drugs. Yes. Some cancer drugs can be damaging to the kidneys - nephrotoxic: http://www.Ncbi.Nlm.Nih.Gov/books/nbk12686/ and: http://www.Ncbi.Nlm.Nih.Gov/books/nbk12686/table/a41774/?Report=objectonly. Cisplatin and Methotrexate are common offenders, but as the table shows, there are others. This needs to be discussed immediately with your oncologist, as im sure you are doing.