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We report measurements down to 16 mK of the electron-spin resonance (ESR) of a sample of silicon doped with phosphorus, of doping density n/n, (at ambient stress) of 0.85. Stress tuning to 0.28 GPa along the (100) direction is used to "tune" the critical doping density n, at the metal-nonmetal transition and thus vary n/n, up to the value 0.91. The electron-spin susceptibility and ESR linewidth vary with temperature below 4.2 K in the same way, and the change in this variation with stress over most of the temperature range shows a strong magnetic-field and frequency dependence at the low fields of our experiments (-10-20 G). This implies that, as the metal-nonmetal transition approaches, the eSect of magnetic field in polarizing the electron-spin pairs becomes rapidly weaker. However, at the lowest temperatures, with or without stress, a cusp develops in the susceptibility versus temperature behavior; we speculate that, so close to the metal-nonmetal transition, the exchange interactions are becoming sufficiently long range for spin-glass behavior to develop. Alternatively, the "rare-spins" scenario, coupled by Ruderman-Kittel-Kasuya-Yosida interactions, of Bhatt and Fisher may be driving the spin-glass behavior. At the low end of the temperature range only about 7% of the electron spins remain magnetically active. The rate of variation of the susceptibility with stress (which tunes n, ) at the lowest temperatures is rather fast, with y varying as n, .