There are plenty of social and collaboration solutions for day to day business: e.g Drupal Commons, Atlassian Confluence, Exo Platform, and many more. They don't really need a "process" to be used, and/or they don't really need to be run through a process. It is the same for social websites like Facebook, Twitter, LinkedIn and more. You use them because it is useful to collaborate, share, and "stay tuned".
The question is more: how can you integrate the social tools used by your customers?
You can use tools like Sprout Social, Mention and others to track what people are saying about your company, its products and services on the Internet. Then, you create alerts with some conditions, schedule events and messages, and produce regular reports for top management. Isn't this a business process for communications and marketing ?
An interesting example is General Motors. They use internal social tools, and have business processes. On the communication side, they cut their advertising budget on social networks a few years ago when they realize that when someone "likes" a car, that doesn't mean they will buy it. However, their community managers check that people are happy with the brands, cars, after sales, and issues they talk about on forums and social networks.
Another example is the after sales and support services of Dell. A few years ago, they were a leading PC manufacturer, and they didn't pay enough attention to people complaining on the Internet when their Dell PCs had issues. Their reputation fell and they lost market share. They created a team to browse forums and social networks to answer, help customers to find solutions, and more. It took them a long time to recover a good reputation.
And to finish with a BPMS example, at Bonitasoft, we have a support case management process for demos. Cases can be started by people in the classic ways (email and phone calls) but also via Twitter. This process listens for Twitter mentions and can even geolocalize origins of issues.
When BPM is about being more efficient about customer satisfaction, social is now one of the keys. And whatever are your choices and strategy, this should already be part of your business, be it B2B or B2C. It is possible to manage this without a BPMS because good solutions already exist. But of course, you can take advantage of the flexibility of a BPMS to create custom social processes if what is available doesn't fit your needs.