  We study the properties of the Bose-Fermi mixture from the perspective of
reaching a state of a self-bound quantum droplet. The variational analysis
shows that the system exhibits bistability. For weak repulsion between bosons,
one of the equilibrium states, smaller in size, spherically symmetric, and with
negative energy, corresponds to quantum droplet, the other with always positive
energy represents the elongated droplet-like state immersed in the sea of a
fermionic cloud. For stronger repulsion between bosons the bifurcation is
seized and only the former state is left. Now it represents an elongated object
which, for strong enough boson-fermion attraction, gets negative energy. It
becomes an excited Bose-Fermi droplet when the trap is released, what is
demonstrated by solving the quantum hydrodynamics equations for the Bose-Fermi
system. To depict our ideas we consider the $^{133}$Cs-$^6$Li mixture under
ideal conditions, i.e. we assume no losses.
