Neff, Rhat for constant looks strange

This seems to be the closest related post I could find (also possibly related: Output for quantities of interest that are actually constants). I have a general question about posterior samples of constants. Sometimes they seem to yield NaN neffs and Rhats, and in the same model other constants has small (but defined) neff and Rhat of 1. The model converges fine and so this is not a critical issue (I assume). I’m just curious what brings about the consistent output.

E.g., in the following output for which m_0 and S_ are user-provided means and covariance matrices of bivariate Gaussians (for two categories each, indicated by the first array dimension), and bias is a user-provided simplex of prior probabilities (for the two categories):

...
m_0[1,1]                 14.00     NaN  0.00    14.00    14.00    14.00    14.00    14.00   NaN  NaN
m_0[1,2]                138.35    0.00  0.00   138.35   138.35   138.35   138.35   138.35     2    1
m_0[2,1]                 61.00     NaN  0.00    61.00    61.00    61.00    61.00    61.00   NaN  NaN
m_0[2,2]                157.91    0.00  0.00   157.91   157.91   157.91   157.91   157.91     2    1
S_0[1,1,1]               81.00     NaN  0.00    81.00    81.00    81.00    81.00    81.00   NaN  NaN
S_0[1,1,2]              106.89    0.00  0.00   106.89   106.89   106.89   106.89   106.89     2    1
S_0[1,2,1]              106.89    0.00  0.00   106.89   106.89   106.89   106.89   106.89     2    1
S_0[1,2,2]            11658.50    0.00  0.00 11658.50 11658.50 11658.50 11658.50 11658.50     2    1
S_0[2,1,1]             6561.00     NaN  0.00  6561.00  6561.00  6561.00  6561.00  6561.00   NaN  NaN
S_0[2,1,2]             -291.27    0.00  0.00  -291.27  -291.27  -291.27  -291.27  -291.27     2    1
S_0[2,2,1]             -291.27    0.00  0.00  -291.27  -291.27  -291.27  -291.27  -291.27     2    1
S_0[2,2,2]              399.11    0.00  0.00   399.11   399.11   399.11   399.11   399.11     2    1
bias[1]                   0.50     NaN  0.00     0.50     0.50     0.50     0.50     0.50   NaN  NaN
bias[2]                   0.50     NaN  0.00     0.50     0.50     0.50     0.50     0.50   NaN  NaN
...

I’m using rstan 2.21.2 (but this output inconsistency has been the case as long as I can remember). I wonder whether it is something that rstan might be able to catch? Thank you and sorry for reviving this old topic.

platform       x86_64-apple-darwin17.0     
arch           x86_64                      
os             darwin17.0                  
system         x86_64, darwin17.0          
status                                     
major          4                           
minor          0.2                         
year           2020                        
month          06                          
day            22                          
svn rev        78730                       
language       R                           
version.string R version 4.0.2 (2020-06-22)
nickname       Taking Off Again