  We construct extensions of the pure-jump $\Lambda$-Wright-Fisher processes
with frequency-dependent selection ($\Lambda$-WF processes with selection)
beyond their first passage time at the boundary $1$. We show that they satisfy
some duality relationships with the block counting process of simple
exchangeable fragmentation-coalescence processes (EFC). One-to-one
correspondences between the nature of the boundary $1$ of the $\Lambda$-WF
process with selection and the boundary $\infty$ of the block counting process
are established. New properties for the $\Lambda$-WF processes with selection
and the block counting processes of the simple EFC processes are deduced from
these correspondences. Some conditions are provided for the selection to be
either weak enough for boundary $1$ to be an exit boundary or strong enough for
$1$ to be an entrance boundary. When the measure $\Lambda$ and the selection
mechanism satisfy some regular variation properties, conditions are found in
order that the extended $\Lambda$-WF process with selection makes excursions
out from the boundary $1$ before getting absorbed at $0$. In the latter
process, $1$ is a transient regular reflecting boundary. This corresponds to a
new phenomenon for the deleterious allele which can spread into the population
in a set of times of zero Lebesgue measure, before vanishing in finite time
almost surely.
