  We introduce a class of birth-and-death Polya urns, which allow for both
sampling and removal of observations governed by an auxiliary inhomogeneous
Bernoulli process, and investigate the asymptotic behaviour of the induced
allelic partitions. By exploiting some embedded models, we show that the
asymptotic regimes exhibit a phase transition from partitions with almost
surely infinitely many blocks and independent counts, to stationary partitions
with a random number of blocks. The first regime corresponds to limits of
Ewens-type partitions and includes a result of Arratia, Barbour and Tavar\'e
(1992) as a special case. We identify the invariant and reversible measure in
the second regime, which preserves asymptotically the dependence between
counts, and is shown to be a mixture of Ewens sampling formulas, with a tilted
Negative Binomial mixing distribution on the sample size.
