If I buy a soft serve of ice cream (a single serving in a cone or tub) and put it in my home freezer, will it retain its shape and texture? What will happen to it?
Soft serve ice cream is soft because:
If you were to freeze soft ice cream, you'd lose the advantage of item 1. In addition, your freezer takes longer to freeze ice cream than an ice cream maker, which may result in ice crystals in the ice cream. Furthermore, once the soft ice cream chills to the freezer temperature (usually around 0F), the lower fat content may decrease the perceived creaminess, because of the information in item 3.
Of course, having said all of that, I haven't tried the experiment, so I'd be interested in hearing first hand stories.
There's a possibility that it develops ice crystals on its surface after some time.
Otherwise, it will still retain its texture (don't expect it to get better!), and its shape.