Is there any way one could store a shapefile inside a geodatabase?
I understand they are two databases from two different times but I recall seeing this done in the past and am curious about how one could replicate it.
A shapefile is a series of files (
*.dbf, etc). It is not a database.
In theory you can store such files in a relational database as Binary Large Objects (BLOBs) but for considerations when doing that see Should binary files be stored in the database? from the DBA Stack Exchange.
I think a much better approach is to import your shapefile into a geodatabase as a feature class.
Shapefiles and geodatabases are two different ways of storing feature classes. A shapefile can contain only a single feature class. A geodatabase can store multiple feature classes.
You can copy a feature class between various different storages, including between shapefiles and geodatabases.
To copy a feature class from a Shapefile to a geodatabase in ArcMap, you can use the 'Feature Class to Feature Class' tool.
Ie, 'ArcToolbox' -> 'Conversion Tools' -> 'To Geodatabase' -> 'Feature Class to Feature Class'
For documentation on this tool, see:
Using this tool to copy the feature class doesn't mean that you are copying the Shapefile itself into the geodatabase, but it means that you are conceptually copying the feature class from within the Shapefile into the geodatabase.
Storing an actual Shapefile in a geodatabase doesn't make sense, so I assumed you mean the feature class rather than the Shapefile itself. If you really want to store the Shapefile in a geodatabase, then see PolyGeo's answer.