I've had a store-bought cheesecake in the refrigerator for four days. Would it be safe to freeze it?
If the cheesecake was fresh when you bought it and your refrigerator is running at 40 degrees or lower, you should be able to freeze it without a problem. Make sure you wrap the cake very well before freezing. I recommend wrapping tightly in plastic wrap and then placing the cake into a bag that you can either seal or tie shut. This will prevent the cake from drying out in the freezer. To thaw the cake, place it in the fridge for a day or two and it should come back to life without a problem.
The downside of freezing and thawing is that your cake may be slightly watery in texture and the crust might lose some of it's crispness. If the cake is wrapped well, the taste should be fine, despite the change in texture.