When I conducted sem using lavaan, I found the variance of a factor was negative. So I fixed the variance of this factor to be zero. Should I fix the covariance with this factor also to be zero? I knew that in Mplus, when one constrained the variance to be zero, its covariance would automatically be zero. Is it necessary to set the covariance to zero?
Fixing negative variance estimates to 0 is not a good idea:
https://doi.org/10.1037/1082-989X.13.2.150
https://doi.org/10.1177/0049124112442138
https://doi.org/10.1037/met0000384
But indeed, lack of variance implies lack of covariance, so you would have to (in lavaan) make that factor orthogonal to be consistent.