The shapefile format has built-in limits on total size, where both the .shp and .dbf are limited to 2,147,483,647 bytes (2^31-1). While you can append to a shapefile so that it exceeds this file size, once you do, it's no longer a shapefile, and many shapefile reader utilities will not function with it.

This means that you probably won't be able to convert the existing dataset to a file format that supports larger data. First you'll need to choose a format (and since .mdb is also limited to 2Gb, the only choice available from your list is file geodatabase). Then you'll need to populate a table ("feature class") in a file geodatabase from the original data source (not the corrupted shapefile). From there, is advisable to "Compact" the FGDB (which will eliminate gaps between records as a result of processing), then to compress it (which will make it read-only and reduce the size a bit more). Finally, you'll need to zip the directory tree with the .gdb suffix.

The file geodatabase format uses a compression algorithm on the vertices, so the storage used by an FGDB will be less than an equivalent shapefile (it also uses variable width attribute records, so if you have any string columns, the attribute component will be smaller as well). If you have unnecessary vertices in your features, you can thin line and polygon features by using the Ramer-Douglas-Peucker line generalization algorithm, as found in the ArcGIS tools Simplify Line and Simplify Polygon (Note: This requires a Standard or Advanced license).

I should point out that you may find difficulty finding a site that will permit a multi-gigabyte upload. It's also questionable that anyone would want to commit to the time it would take to download such a massive file. So you may want to review your purpose in such an upload before you invest in the time to construct such a file.

The shapefile format has built-in limits on total size, where both the .shp and .dbf are limited to 2,147,483,647 bytes (2^31-1). While you can append to a shapefile so that it exceeds this file size, once you do, it's no longer a shapefile, and many shapefile reader utilities will not function with it.

This means that you probably won't be able to convert the existing dataset to a file format that supports larger data. First you'll need to choose a format (and since .mdb is also limited to 2Gb, the only choice available from your list is file geodatabase). Then you'll need to populate a table ("feature class") in a file geodatabase from the original data source (not the corrupted shapefile). From there, is advisable to "Compact" the FGDB (which will eliminate gaps between records as a result of processing), then to "Compress" it (which will make it read-only and reduce the size a bit more). Finally, you'll need to zip the directory tree with the .gdb suffix.

The file geodatabase format uses a compression algorithm on the vertices, so the storage used by an FGDB will be less than an equivalent shapefile (it also uses variable width attribute records, so if you have any string columns, the attribute component will be smaller as well). If you have unnecessary vertices in your features, you can thin line and polygon features by using the Ramer-Douglas-Peucker line generalization algorithm, as found in the ArcGIS tools Simplify Line and Simplify Polygon (Note: This requires a Standard or Advanced license).

I should point out that you may find difficulty finding a site that will permit a multi-gigabyte upload. It's also questionable that anyone would want to commit to the time it would take to download such a massive file. So you may want to review your purpose in such an upload before you invest in the time to construct such a file.