InDesign offers several ways to handle this. Which works best for you will depend on your particular circumstance.
CONDITIONAL TEXT --
In CS4 and later, there is a feature known as "Conditional Text" (link is to the Adobe online help page -- scroll down to find the Conditional Text entry). This allows you to designate sections of text to be shown or not, based on criteria you select. It takes a bit of planning up front, but once you've baked it into your document you can turn sections on and off to export different versions.
There are videos on Adobe TV that demonstrate this feature.
ALTERNATE LAYOUT --
In the Pages panel, you can create and name custom layouts. This feature, which came in with InDesign CS5.5, if I recall, is intended for use with Adobe's Digital Publishing Solution for tablet publishing, but it has other uses.
Once your "Master" document is done, you can create an alternate layout for each of the "subset" documents. They all reside in the same file, side by side in the Pages Panel, and you can switch from one to the other to work on it.
Every item in an alternate layout is linked to its original in the "master document" from which you started, so that any edits made to the original will be reflected in the copies (you'll need to update the links in the same way that you would update any link).
Deleting pages from an alternate layout poses no problems for you page numbering. You can also, if necessary, specify that each alternate have its own folder of text styles, so you can change them independently of the original.
For export to PDF, you would select the version you want to export in the initial export dialog.
PLACE AND LINK --
InDesign CS6 and CC have a function under the Edit menu,
Place and Link. This works in conjunction with the Content Conveyor Tool, but can be used without invoking the Content Conveyor first.
Although Place and Link was originally conceived to work within a single document, it also works across documents.
In this workflow, you would again create the master document, but instead of using Alternate Layouts you would create separate "subset" documents, and using the Content Conveyor or "Place and Link" populate these with the correct pages from the master.
Any time you save changes to the master, each affected subset document will display the out-of-date link warning, and you would update the stale link(s) in the usual way.
XML STRUCTURE --
This is the industrial strength method, not for the faint of heart and not necessary in cases, but when you need it, it can speed up automated document production enormously. In one case on record (a wine catalog, produced annually), total production time was cut by 85% (not a typo) by switching to XML.
This is far too complex to go into here. Adobe has material online, and I recommend the excellent "A Designer's Guide to Adobe InDesign and XML" by James Maivald has a permanent place on my bookshelf.