As this process is repeated the excess must continue to grow from 100,000 to 111,111, and the value of the money piece in terms of bullion continue to fall from 10 to 9.

At this point the 111,111 pieces would contain just the same amount of bullion and have just the same value as the 100,000 pieces did before.

Thereafter no further profit would accrue to the government from issuing coins of that weight.

To make a further profit it must again reduce the amount of pure metal in the coin.
This process was often repeated in the Middle Ages.

A ruler, either by making a higher seigniorage charge or by coining on his own account, debased the quality or reduced the weight of the money of his realm.
For a time the new coins, having the same monetary use, circulated at par with the old coins.