There are very few silver mines. Most silver comes from mining other metals such as copper, zinc, and gold. They make their money from the primary metals so they dump the silver at the market. Even if the market was $5 they will sell it because is an extra. Therefore, no matter how cheap silver gets, they will keep mining copper, etc. Therefore, if silver mines close because they are not profitable, there will still be a lot of silver from mining other metals.
The problem with the price of silver is the huge supply acquired from mining other metals and that there is very little demand. All the large uses of silver are no longer. That is, little or no photography using silver and almost no silverware, The USA and many other countries no longer use silver coins as money, and there is very little silver used anymore in jewelry.
Because of the huge supply and so little usage, don't be surprised if the price of silver falls to $10 per ounce.