I have a C1/D visa, which I have used to work on cruise ships for over 3 years. Never overstayed or anything and I have an ESTA to travel to the USA. This trip, I overstayed by 1 month. Will the C1/D be cancelled and impossible to renew in the future, even with an employment letter?
Legally speaking, an overstay on the Visa Waiver Program does not directly affect the validity of a visa that you have. However, any time you try to enter the US on most types of nonimmigrant visas, you have to satisfy the officer that you do not have immigrant intent, and past immigration violations are certainly a negative factor in the officer's determination.
The visa may have not been automatically cancelled but next time you try to enter the USA, your previous overstay will likely pop up on the CBP officer’s computer and you’ll be denied entry, your visa will be cancelled, and you’ll be refused entry.
That’s the worst case scenario.
You could look up your I94 record online and see if your departure was recorded but if it wasn’t, that may lead to more questions that you can’t answer without leading to the above scenario.
As @Patricia Shanahan notes, it’s much better to overstay less than 180 days so if you are still in country, try to leave as soon as you can.