I get again confused by fixed and random. See here Looic and elpd_diff (rstanarm model) - #2 by avehtari reasons for not to use those and what would be better terminology.
If you have several observations from a participant(?) indexed by PID, then after removing just one observation, it’s still easy to predict that based on the other observations from that participant. If you want to examine the effect of the population mean, then you would need to leave-out all observations for one participant at time. Then you could see the difference whether the population mean is zero (model Un~ (1 + Entrenchment |PID) + (1|Verb)) or non-zero (model Un~ (1 + Entrenchment |PID) + (1|Verb) + Entrenchment).
To implement leave-one-participant-out cross-validation you need to do some coding.
@jonah for rstanarm it would be great to have option for kfold to make the data division based on given variable, like in this case PID, to make leave-one-group-out easy.