Do people get cancer of the urethra, and if so, how rare is it?

Urethra cancer. People can get cancer of the urethra. There are different types ranging from urothelial carcinoma to adenocarcinoma to others. All of these rumors are very rare. If you think you have a tumor in this region, seek a doctor's advice for work-up.
It is relatively. Rare; more related to chronic irritation, like an indwelling catheter, but both men and women can get it. I have seen a half dozen cases in a 35 year career: none has done well.