Suppose we do rejection sampling. Then the universe restarts at 2000 every time a datapoint is violated. The subjective experience of entities inside such a simulation would be best described as random death with occasional survival if some arbitrary criteria are met. Writing (long-lasting) believable false reports will alter the criteria to include those reports somehow being written.

MCMC algorithm is more interesting. It introduces a strange contortion of time; we generate an initially random space-time with the known datapoints clamped, and then re-sample the unknown bits for a long time to get a good posterior distribution over the possibilities. Real time is a sometimes-nonsensical meandering through possibility-space. Time as experienced "in the simulation" is relatively normal, but it is interesting/boring to argue about whether entities living in such a simulation have experiences in a meaningful sense. Causality doesn't work at all as it should, but it will appear to work roughly as it should most of the time. Events will conspire to bring about a random assortment of facts which are the clamped values, but the better-quality samples will make the conspiracies look like true chance.

Metropolis-hastings is an even more advanced technique, but I don't think there is anything special about the subjective experience if the simulated entities in MH as compared to basic MCMC.