  The detection of a 0.2 Msun extremely low-mass white dwarf (EW) in a wide
orbit (Porb about 450 days) with a 1.1 Msun main-sequence (MS) companion, KIC
8145411, challenges our current understanding of how EWs form. The traditional
channel for EW formation, via mass transfer from the WD progenitor, is expected
to form EW binaries in tight orbits. Indeed, the majority of known EWs are
found in tight binaries with a median Porb about 5.4 hrs. Using numerical
scattering experiments, we find that binary-binary strong encounters in star
clusters can sufficiently widen the orbit of a typical EW binary, to explain
the observed wide orbit of the KIC 8145411 system. The Porb distribution for EW
binaries produced through binary-binary encounters is bimodal: one mode
corresponds to the initial orbital period of the EW binary, while the other is
near Porb about a few 100 days, similar to the orbital period of the KIC
8145411 system. We find that the production of wide EW binaries that are also
ejected from the cluster peaks at a star cluster mass of about 10^5 Msun with a
rate of about 10^{-3} Gyr^{-1}. Assuming that 50% of all stars form in star
clusters and an initial cluster mass function proportional to m^{-2}, we
estimate a galactic formation rate of about 4.16 x 10^3 Gyr^{-1} for wide EW
binaries.
