  We present the orbital solution of a peculiar double-lined spectroscopic and
eclipsing binary system, 2M17091769+3127589. This solution was obtained by a
simultaneous fit of both APOGEE radial velocities and TESS and ASAS-SN light
curves to determine masses and radii. This system consists of an
$M=0.256^{+0.010}_{-0.006}$ $M_\odot$, $R=3.961^{+0.049}_{-0.032}$ $R_{\odot}$
red giant and a hotter $M=1.518 ^{+0.057}_{-0.031}$ $M_\odot$,
$R=2.608^{+0.034}_{-0.321}$ $R_{\odot}$ subgiant. Modelling with the MESA
evolutionary codes indicates that the system likely formed 5.26 Gyrs ago, with
a $M=1.2$ $M_\odot$ primary that is now the system's red giant and a $M=1.11$
$M_\odot$ secondary that is now a more massive subgiant. Due to Roche-lobe
overflow as the primary ascends the red giant branch, the more evolved
"primary" (i.e., originally the more massive star of the pair) is now only
one-sixth as massive as the "secondary". Such a difference between the initial
and the current mass ratio is one of the most extreme detected so far.
Evolutionary modelling suggests the system is still engaged in mass transfer,
at a rate of $\dot{M} \sim 10^{-9}$ $M_\odot$ yr$^{-1}$, and it provides an
example of a less evolved precursor to some of the systems that consist of
white dwarfs and blue stragglers.
