Depending on the project, this could be the end of their involvement, or they can be heavily involved every day. The line producer is the person brought in to prepare the budget, and execute it. That has since been shortened to line producer. That bit of history out of the way, I like to think of the term line producer a little differently, and this is where we start getting into the distinction between a line producer and a production manager. This is the area of responsibility.
Different studios use slightly different forms, but the basic lines remain the same.
Oddly, I have always found the HBO form, available in Movie Magic Budgeting, to be the most useful in independent films. This is because it has less of the studio overhead. Because the line producer prepares the budget, he should really be the only one who is allowed to adjust it. Budgets always need adjusting. When you prepare the budget, you haven't hired the crew or seen a location.