Comparing unbalanced groups with ANOVA/Kruskal-Wallis when one group has only 1 observation

I would like to compare a continuous variable across 5 health status groups, but one of the groups has only 1 observation. Would an ANOVA/Kruskal-Wallis be valid? What can I do about the group with only 1 observation?

The boxplots for the continuous variable across the groups look as follows:

The group sizes are:

A: 12B: 8C: 9D: 7E: 1

Background info: I work in biostatistics and my datasets are fairly small, and some outcomes are rare in biology. Collecting samples is also dependent on patients and is an expensive procedure, so getting a larger sample is not a feasible solution.

Edit: What I currently do is to omit the group with only one observation in my analysis, however I am not sure about the validity of that.