The bitcoin network adjusts its difficulty. If there is no other miners, then my old laptop is all that is needed to keep the bitcoin network alive, still finding blocks on average every 10 minutes. And there will always be at least one old machine mining.

There is a problem with having  a very low difficulty though, and it is low security. Someone with more hashing power could do a 51% attack and steal coins. 

But do not worry. As long as bitcoin has any value, the mining will continue.