The answer is, "It depends." If your family or villagers die, the game will generate new peeps for you, and you can continue with your game with your "stuff" exactly as it was. If you delete your game from your device, however, that will delete all of your purchases, along with everything you had achieved in your game. Although you can reinstall the game for free, some In-App Purchases you made may be lost. This is due to how Apple has set up their store.
There are several kinds of In-App Purchases that Apple has set up for developers to offer in the App Store, which you can read about in
Apple's guide to In-App purchases. Apple explains how each type of purchase is handled by the App Store.
Our games use two of those types of In-App Purchases: non-replenishable and replenishable. Coins and tech points, for example, are non-replenishable and get used up as you spend them. They will also be deleted if you delete the game, and they cannot be re-downloaded for free. The "doublers" in VV: Origins and Food Club, Brokerage Account, and Medical Plan in VF2 are replenishable and can always be re-downloaded for free once they have been purchased.
But basically, whatever you buy in the game stays as long as you don't delete the game from your device.