Sampled parameter dropping at the last iteration

I am wondering if there could be a generic cause of this sampling behaviour (that I have encountered in the past but I never wondered too much on) and/or could be indicative of some common pathology .

Warning message

Warning messages:
1: There were 3 chains where the estimated Bayesian Fraction of Missing Information was low. See 
2: Examine the pairs() plot to diagnose sampling problems

My model

data {
  int<lower=0> N;
  int<lower=0> G;
  int<lower=0> counts[N,G];
  real my_prior[2];
  int<lower=0, upper=1> omit_data;

parameters {

  // Overall properties of the data
  real lambda_mu;
  real<lower=0> lambda_sigma;
  real<lower=1> sigma;

  // Gene-wise properties of the data
  vector[G] lambda;

model {

  // Overall properties of the data
  lambda_mu ~ normal(0,1);
  lambda_sigma ~ cauchy(0,2);
  sigma ~ gamma(3,2);

  // Gene-wise properties of the data
  lambda ~ normal(lambda_mu, lambda_sigma);

  // Sample from data
  for(n in 1:N) counts[n,] ~ neg_binomial_2_log(lambda, sigma);

generated quantities{
  int<lower=0> counts_gen[N,G];
  vector[G] lambda_gen;

  // Sample gene wise rates
  for(g in 1:G) lambda_gen[g] = normal_rng(lambda_mu, lambda_sigma);

  // Sample gene wise sample wise abundances
  for(n in 1:N) for(g in 1:G) {
    counts_gen[n,g] = neg_binomial_2_log_rng(lambda_gen[g], sigma);


Using 1/sqrt(phi) as the precision prior with negative binomial, as suggested in I overcome such strange behaviour.

However the curiosity remains: how come sigma that is constrained > 1 drops below 1 at the final stage of sampling.