I have a grid in witch some rows are visible and some not.
When I type a the column of the grid to find specifics rows (built-in search-as type), the search filter is applied on the visible rows only. That is correct.
When I use the backspace to empty the search string text box then the visible and the hidden rows are shown.

Thank you.
The built-in search-as-type changes the same Visible property for every row while searching, so Visible is set to True for ALL rows if you have no search text.

As a possible idea (but it should be checked) you could use custom match rule for search-as-type to always exclude rows you made originally invisible. In this case you will also need to store the original visibility state somewhere else.

Another idea is to implement your own search-as-type through an external textbox, when you can process filtering the way you need.