Shrunken dimension table is a specific type of a dimension in Kimball DW design. Let's explain the purpose of shrunken dimension based on an example. If you have Sales fact table with SalesRepresentativeID that comes from SalesRepresentative dimension; you may want to record targets but not for sales representive but for region of the sales representative. How to design it?
You need SalesRegionTarget fact table on region granularity level and you need to connect it to SalesRegion dimension and because you already have Region attribute in SalesRepresenative dimension that describe lower level attribute (representative) you can re-use it. There are two ways to re-use it
First approach is to create SalesRegion based on SalesRepresentative dimension in a standard way. You put surrogate key and put Region as business key and extract data from SalesRepresenative dimension.
The second approach applies when you have slightly more normalized DW and you have RegionID and RegionName. In this can you can just build the dimension based on existing objects and populate fact table in the usual way.
The third approach as pointed out by "gurvimail" is to normalize the dimension (similar to second approach) and have regions join to Sales Representative dimension instead of fact table but let's bear in mind that main purpose of shrunken dimension in our case is to join to higher level granularity fact table so with third approach we wouldn't be able to use Sales Representative dimension for Targes fact table.