(Abridged) We present an analysis of ionization and metal enrichment in the Magellanic Stream (MS), the nearest gaseous tidal stream, using HST/STIS and FUSE ultraviolet spectroscopy of two background AGN, NGC 7469 and Mrk 335. For NGC 7469, we include optical spectroscopy from VLT/UVES. In both sightlines the MS is detected in low-ion and high-ion absorption. Toward NGC 7469, we measure a MS oxygen abundance [O/H]_MS=[OI/HI]=-1.00+/-0.05(stat)+/-0.08(syst), supporting the view that the Stream originates in the SMC rather than the LMC. We use CLOUDY to model the low-ion phase of the Stream as a photoionized plasma using the observed Si III/Si II and C III/C II ratios. Toward Mrk 335 this yields an ionization parameter log U between -3.45 and -3.15 and a gas density log (n_H/cm^-3) between -2.51 and -2.21. Toward NGC 7469 we derive sub-solar abundance ratios for [Si/O], [Fe/O], and [Al/O], indicating the presence of dust in the MS. The high-ion column densities are too large to be explained by photoionization, but also cannot be explained by a single-temperature collisional-ionization model (equilibrium or non-equilibrium). This suggests the high-ion plasma is multi-phase. Summing over the low-ion and high-ion phases, we derive conservative lower limits on the ratio N(total H II)/N(H I) of >19 toward NGC 7469 and >330 toward Mrk 335, showing that along these two directions the vast majority of the Stream has been ionized. The presence of warm-hot plasma together with the small-scale structure observed at 21 cm provides evidence for an evaporative interaction with the hot Galactic corona. This scenario, predicted by hydrodynamical simulations, suggests that the fate of the MS will be to replenish the Galactic corona with new plasma, rather than to bring neutral fuel to the disk.
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