I know that the majority of people use standardized encryption ciphers such as AES-256, and for good reason. But what I want to know is if anyone has come across a company or organization that is selling their own proprietary symmetric encryption algorithm. I'm doing research on this specific use case and would appreciate some help.
Yes. One prominent commercial example is Cypto AG, a company in switzerland. Its clients include some nation states. Of course most major nation states have their own proprietary diplomatic and military symmetric key algorithms.
See the Crypto AG website here.
Historically, they have been involved in some controversies. See one example report here.
Googling will yield much more on Crypto AG and its history, usual caveats apply. The main objection is lack of open peer review.
Edit: References to Crypto AG's proprietary algorithms are given below. I am not claiming these are secure algorithms, FWIW.
The link here has a company document from 2007:
"For encryption, the proprietary HCA-480 crypto algorithm is used in combination with Customer Managed Profiling (CMP), offering a variety of over 10506. The Communication Key (CK) is 128 bits long and is used to generate a key stream with a period of more than 1028 years."
A newer link is here:
"All systems are based on the sophisticated Crypto Security Architecture, which comprises elements such as a tamper-proof hardware module, customer-controlled and proprietary algorithm [..] emanation-proof hardware (COMPREM) and a flexible security and network management."