The formation of deeply-bound antikaonic $K^-/bar{K}^0$ nuclear states by nuclear ($K^-$, $N$) reactions is investigated theoretically within a distorted-wave impulse approximation (DWIA), considering the isospin properties of the Fermi-averaged $K^-+ N to N + bar{K}$ elementary amplitudes. We calculate the formation cross sections of the deeply-bound $bar{K}$ states by the ($K^-$, $N$) reactions on the nuclear targets, $^{12}$C and $^{28}$Si, at incident $K^-$ lab momentum $p_{K^-}$ = 1.0 GeV/c and $theta_{rm lab} = 0^{circ}$, introducing a complex effective nucleon number $N_{rm eff}$ for unstable bound states in the DWIA. The results show that the deeply-bound $bar{K}$ states can be populated dominantly by the ($K^-$, $n$) reaction via the total isoscalar $Delta T=0$ transition owing to the isospin nature of the $K^-+ N to N + bar{K}$ amplitudes, and that the cross sections described by ${rm Re}N_{rm eff}$ and ${rm Arg}N_{rm eff}$ enable to deduce the structure of the $bar{K}$ nuclear states; the calculated inclusive nucleon spectra for a deep $bar{K}$-nucleus potential do not show distinct peak structure in the bound region. The few-body $bar{K}otimes [NN]$ and $bar{K}otimes [NNN]$ states formed in ($K^-$, $N$) reactions on $s$-shell nuclear targets, $^3$He, $^3$H and $^4$He, are also discussed.
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