This one is difficult. Also included in this scenario is when a buyer contacts the seller directly. You won't be able to recognize this situation when it comes up because it's not always advertised. If you are able to jump in though, you can convince the home seller that they might be missing out on a good amount of money by selling to a loved one. Offer to send them a home valuation, and sell their home for more -AND- help their friend or relative find another home within their price range!
This is fair. Try to appeal to their sense of logic, and give them the numbers of what recent homes sold for in their area. Also include the necessary costs to advertise the home. Then talk about the possible legal costs incurred if they get sued over the sale. They would not only be saving money, but they would be earning more by utilizing your real estate services.
Of course they don't want to deal with an agent! That is why they choose the FSBO lifestyle in the first place! I'm sure having to regularly field cold calls doesn't help either. There are many approaches to take with this, and you should choose one that works for you. At the end of the day when their home doesn't sell, they will have an increased desire to work with an agent. That is when your lead nurturing skills come into play, and the value you have been providing them will push them to pick you over the other agents.
Maybe they did work with an agent previously, and the agent did such a bad job they think they could do it themself? Use your impeccable phone skills to get the FSBO into a conversation, and explain to them why the home didn't sell..and how you can get the home off the market. It sounds easy on paper...but keep in mind, they worked with an agent before so that means they are more likely to work with another one in the future, if the right person presents themself.