We present photometric and spectroscopic observations of the 03fg-like type Ia supernova (SN Ia) ASASSN-15hy from the ultraviolet (UV) to the near-infrared (NIR). ASASSN-15hy shares many of the hallmark characteristics of 03fg-like SNe Ia, previously referred to as super-Chandrasekhar SNe Ia. It is bright in the UV and NIR, lacks a clear i-band secondary maximum, shows a strong and persistent C II feature, and has a low Si II $lambda$6355 velocity. However, some of its properties are also extreme among the subgroup. ASASSN-15hy is under-luminous (M$_{B,peak}=-19.14^{+0.11}_{-0.16}$ mag), red ($(B-V)_{Bmax}=0.18^{+0.01}_{-0.03}$ mag), yet slowly declining ($Delta{m_{15}}(B)=0.72 pm 0.04$ mag). It has the most delayed onset of the i-band maximum of any 03fg-like SN. ASASSN-15hy lacks the prominent H-band break emission feature that is typically present during the first month past maximum in normal SNe Ia. Such events may be a potential problem for high-redshift SN Ia cosmology. ASASSN-15hy may be explained in the context of an explosion of a degenerate core inside a non-degenerate envelope. The explosion impacting the non-degenerate envelope with a large mass provides additional luminosity and low ejecta velocities. An initial deflagration burning phase is critical in reproducing the low $^{56}$Ni mass and luminosity, while the large core mass is essential in providing the large diffusion time scales required to produce the broad light curves. The model consists of a rapidly rotating 1.47 $M_{odot}$ degenerate core and a 0.8 $M_{odot}$ non-degenerate envelope. This deflagration core-degenerate scenario may result from the merger between a white dwarf and the degenerate core of an asymptotic giant branch star.
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