$S_(N)1$ reactions are essentially BOND-BREAKING reactions, that proceed thru the intermediacy of a three-membered intermediate. And we could examine the solvolysis of say a benzyl halide....
$PhCH_2X stackrel"slow"rarrunderbrace(PhCH_2^(+))_"benzyl carbocation" + X^-$
And such a species could undergo solvolysis...i.e. with the alcoholic or aqueous solvent....
$PhCH_2^+ + ROH stackrel(-H^+)rarr PhCH_2OR$
But you should digest the relevant chapter in your text....