I notice that for the 3,644,409 employed NYC residents (EMPSTAT =1), substantially fewer of the employed have a IND code compared to a INDNAICS code. The difference is 725,980 persons have a ‘0’ code for IND but none of the employed have a ‘0’ code for INDNAICS.
I am afraid I was not able to replicate your observation. Using the 2011 5yr ACS sample I could not identify any respondents with EMPSTAT==1 who also had IND==0. Furthermore, all individuals coded IND==0 also had INDNAICS==0.
I am not sure if this is a recoding error or if the dataset was not completely decompressed. I would recommend re-downloading the data, decompressing the data using appropriate software (such as 7-Zip), and attempting your analysis again.