  We propose an extension of the classical $\Lambda$-Fleming-Viot model to
intrinsically varying population sizes. During events, instead of replacing a
proportion of the population, a random mass dies and a, possibly different,
random mass of new individuals is added. The model can also incorporate a drift
term, representing infinitesimally small, but frequent events. We investigate
elementary properties of the model, analyse its relation to the
$\Lambda$-Fleming-Viot model and describe a duality relationship. Through the
lookdown framework, we provide a forward-in-time analysis of fixation and
coming down from infinity. Furthermore, we present a new duality argument
allowing one to deduce well-posedness of the measure-valued process without the
necessity of proving uniqueness of the associated lookdown martingale problem.
