Hi Frank -
Great question. I added a little info to an appendix about this as I think it is a pertinent question. I added the appendix to the Github here:
https://github.com/saudiwin/ordbetareg/blob/master/kubinec_ord_betareg_appendix.pdf
The cutpoints are weakly identified by the prior (i.e., the difference between them is Normally distributed), so it is really OK to fit a model with no observations at the bounds (or just one bound). It’s probably better to do so in the likely case that future iterations of your data could have observations at the bounds. You would need to have data that you were sure did not have any observations at the bounds (something where the probability of the data vanishes as the bounds approach).
The cutpoints will simply be estimated at far ends of the latent scale, and you will be able to generate them from the posterior predictive distribution with small probability. As such, it’s not a bad thing to have them as you could later combine data from future samples that have such observations at the bounds (or create realistic predictive data with observations at the bounds).
Let me know if you have any other questions!