Activities are usually already split on a day by day basis on most schedules. The split already happens on non-work hours and days such as week-ends, holidays etc. All you have to do is add non-work calendar exceptions to you activity calendar, preferably an individual calendar as not to impact other activities you do not want to.
Then by necking you will be able to see when activity will split after DD, either an ongoing or a future split.
Depending on software you might not be able to see splits on past performance bars but with use of histograms you will.
This method does not add new activities, will keep all logic, costs etc valid.
For permanently suspended activity use appropriate RD or actual finish date and adjust remaining duration and cost data as required.
For temporary suspension with unknown resume date on every update add required non-work days up to update DD.