Chemotherapy targets fast replicating cells as tumours grow quickly. Your nails, hair, digestive tract and skin cells replicate very quickly too and most chemotherapy treatments cannot tell the difference between nails and tumours so it attacks nails too, often causing damage.
There are ways in which you can prevent damage, with the consent of your medical team. If the use of cooling gloves and slippers is not an option for you, try using nail oil, three times a day from the start of chemotherapy. It has been shown to reduce nail damage. If the appearance of your nails or nail bed changes, use nail varnish to camoflauge the damage.