The subscriptions for a product will be managed by periods, appended together.

See the following example time-line.

After the first purchase, a subscription period will be started (Period 1). If the period expires, the customer will no longer have access to the product.
After some time, the customer buys the product again and a new period will start (Period 2).
Now, the customer buys another subscription period, while the current period is stil lrunning (Purchase 3). Since Period 2 has a end-date in the future, the start of the 3rd period will be set to the end date of the last period at this time.

By the way, this will also happen if a customer buys a product with different subscription periods.