How to interpret semivariogram with range but no partial sill?

I have been using the variofit function in R's gstat package to fit semivariogram models to some spatial data I have, and I am confused by a couple of the models that have been generated. Basically for these few models, I will get a model that has a range for autocorrelation, but not a partial sill. I was told that even without a sill, though, the model should still have some sort of shape to reflect the range, but plotting this model results in the flat lines that are shown in the attached screenshot. I do not think it is a matter of bad initial values as I let variofit parse out the best initial values from a matrix of many values made by expand.grid. I wanted to know whether this is being plotted correctly contrary to what I've been told, and what exactly it means to have a range but no partial sill value. I know when I used an alternative model fitting function from geoR (fit.variogram), these models could be fit to a periodic or wave distribution, though poorly so/probably overfit — so would this be some indication of that, which variofit just cannot plot? I unfortunately can't share the data, but I included an example of the code I have used to make these models if it will help to answer my question:

geo.entPC <- as.geodata(cbind(jitteryPC, log.PC[,5], coords.col=1:2, data.col=5))

test.pc.grid2 <- expand.grid(seq(0,2,0.2),seq(0,100,10))

variog.function.col2 <-function (x) {
  vario.cloud <- variog(x, estimator.type = "classical", option="bin")
  variogram.mod <- variofit(vario.cloud , ini.cov.pars=test.pc.grid2,  fix.nug=FALSE, weights="equal")
  plot(vario.cloud)
  lines(variogram.mod, col="red")
  summary(x)
 
  
}

variog.function.col2(geo.entPC)

From the attached plot showing the empirical variogram, I would not expect to find any sensible spatial correlation. This is in accordance with the fitted variogram, which is essentially a pure nugget model. The spatial range might be a relic of the numerical optimization, or the partial spatial sill might (numerically) differ from 0 at a digit that is not shown in the summary of the fitted variogram. However, no matter what the range is for an irrelevant small partial sill, the spatial correlation is neglectable.

Depending on the data, it is sometimes beneficial to limit the maximum distance of pairs used to calculate the empirical variogram - but make sure to have "enough" pairs in each bin.