SN1 vs SN2 in low concentration of nucleophile
Let us assume that the competing reaction is a Sn2 based pathway.

Sn2=k[substrate][nucleophile]

Sn1=k'[substrate]

Relative rate of products formed=(ie.. Sn1 to Sn2 product)=k'/(k[nucleophile]

Sn1 Reaction doesnot depend on concentration of the nucleophile , so more the concentration of nucleophile, the relative rate of Sn1 product diminishes.

Hence ,when the competing reaction is a Sn2 pathway, lesser concentration of nucleophile would favour the Sn1 pathway.

Hope this helps.