The supply of silver cannot be predicted with certainty. The world could run out of silver at some point, but this also happens with other precious metals such as gold and platinum. However, it is not possible to accurately predict when this might happen with any degree of certainty. Without the essential life force that is silver, we will undoubtedly find ourselves in a world of problems.
Unfortunately, that new world is rapidly invading an already extremely limited economic environment. At the current rate, it is estimated that by 2028, the Earth will have completely run out of economically extractable silver reserves.