Using Actual NULL Values
Shapefiles cannot handle NULL values so copy the feature class to a file geodatabase. Then in the new copied fGDB feature class, view the attribute table, and right-click on the field heading and choose 'Field Calculator`.
In the Field Calculator options, set the options as per below (replacing 'fieldName' with the actual name of the field):
Show Codeblock: ON
Pre-Logic Script Code (appears after setting 'Show Codeblock' ON above):
if value == -9999:
fieldName = : calc(!fieldName!)
None is the Python way of specifying the NULL value.)
Alternatively, you can first select only the records with the -9999 values, and then in the Field Calculator just select 'Python' and enter the expression as
None. The Field Calculator will only run on the selected records (if there are any selected). This is simpler to implement but my personal preference is to use the method described above, as it has all the logic in one place.
Using Another Value Instead of NULL
If you don't explicitly need NULL but some other value will do (eg, and empty string, '', or 0), then you don't need to copy to a fGDB first. But I'd still recommending using a copy of the data (eg copy to a new shapefile) to avoid corrupting your original data. In this case, use the Field Calculator as above, but, replace
return None with