Hi Alfredo,
There isn't a standard way to read the same file sequentially. The easiest way is to read the file once the day is over because a OS batch that read partially generating a new file to be picked to PI seems to complicated for me.
However, if your scenario is file - RFC (or proxy), the control could be developed in the endpoint system or during mapping you can use RFC lookup or jdbc lookup to take the number of lines of the last execution and do another RFC lookup or jdbc lookup to store the new value (total lines).
Regards.