Wow, CP is super knowledgable about exactly what circumstances enable you to keep getting checks for a child who no longer lives with you.
Unfortunately, if the info she quoted is accurate, it sounds like it may have been legal for them to keep receiving the checks. (At least in their claimed fantasy scenario of Erica living "out of home" but rights not terminated.) I'm sorry to say so, but don't shoot the messenger.
It's very striking, though, that their explanation of her disappearance does fit the terms of what would legally enable them to keep collecting checks. Almost like they researched it after the first time they sent her away and then got worried about the checks.