We have investigated the nature of P Cygni-like features in the high-resolution IUE spectra of the symbiotic variables BF Cygni and EG Andromedae by looking for orbital phase-dependent variations in the structure and velocity of the C IV (1550 angstrom) resonance doublet in 10 archival IUE high-dispersion spectra of these systems and by comparing their profiles with P Cygni-like features seen in IUE high-dispersion spectra of other symbiotic stars. For BF Cyg, we find maximal P Cygni absorption equivalent widths and terminal velocities of approximately 900 m angstrom and approximately -240 km s-1, respectively, full emission velocity widths at the 10% intensity level of 300-400 km s-1, depending on phase, PHI, variations in the width of the P Cygni absorption, shortward velocity shifts of the C IV emission line in all but two orbital phases, relative to the C IV velocity at PHI = 0.01, and absorption substructure within the C IV P Cygni lines which coincide in velocity from image to image. In EG And the C IV P Cygni absorption equivalent width is, on average, 300 m angstrom with a terminal velocity of -217 km s-1 (which includes the systemic radial velocity contribution of -93 km s-1). The presence in one image, of a strong absorption feature at He II (1640), having a precise velocity coincidence with the C IV P Cygni absorption component, suggests that the absorbing material responsible for both line features is associated with outflow and P Cygni self-absorption from the vicinity of the hot component. In both BF Cyg and EG And, the structure and behavior of the P Cygni profiles may rule out their origin in the red-giant wind or in an expanding circumbinary shell. Our results support the hot-component wind interpretation of Mikolajewska et al. Motivated by the low-mass white dwarf shown to be present in BF Cyg (Mikolajewska et al.), we have carried out quasistatic evolutionary model calculations with accretion onto a 0.55 M. white dwarf accreting at the rate 2 x 10(-8) M. yr-1. The sequence of 3800 quasistatic models, the first to be reported for a low-mass hot white dwarf (M(wd) < 0.8 M.) accreting at a high rate, yields an unexpected outburst behavior in response to accretion at that rate, when compared to evolutionary sequences with accretion onto higher-mass white dwarfs. A series of three major thermonuclear shell flashes and one lower-energy shell flash is revealed with the timescale during outburst and the interoutburst timescale substantially shorter than expected for a 0.55 M. white dwarf. Implications for the observations of symbiotic systems thought to contain low-mass white dwarfs, are discussed.