Yes, it can happen. Some people misunderstand social media and how to make it work for them thus social media can backfire and work against them; this applies to both large and small companies. Even though social media is a free tool to utilize that does not mean you should jump on board without a plan and doing your research first!
To begin, you need to understand where your target market is in the social media realm. You also need to understand how you can join their conversation. Research to understand what your target market is talking about and how you can begin facilitating a conversation that involves your brand. But always keep in mind that not all the conversation will be positive. It is still your responsibility as a progressive marketer to address negative conversation, not ignore it!
So here are just a few things that can lead to social media suicide: ill preparation & ill research, lack of understanding and failing to address negative feedback. The list is actually more extensive but I will save that for another time. These are just a few things to consider when making the choice to enter social media marketing.
Keep in mind that you are no longer 100% in control of your brand. Your social network will be participating in brand conversation and as a marketer it's your responsibility to guide that brand conversation to meet strategic goals and reputation management. So learn to understand how to guide the brand and save yourself from social media suicide!