I definitely remember such a system at my municipal public library:
The machine would nibble out a bit of the edge on each pass, so that the next time the card would go into the machine slightly farther.
The size of the nibble related directly to the printed date, etc. entered on that line.
Before that, smaller libraries had the name of the patron hand-written in a cell on a non-mechanical card. One could check if any famous professor had borrowed the same book.