Why do we liquefy when we also solidify (but not soledefy)?

I don't think this is explained by any English rule. It's just based on etymology.

The spelling liquify actually exists as a variant.

In terms of etymology, the Latin source of liquefy is liquefacio, which is supposed to have been derived from compounding the verb liqueo with facio. A similarly formed (now obsolete in English) word is calefy, where the first part comes from the Latin verb caleo. Putrefy may also be analogous.

In contrast, the Latin ancestor of solid, the adjective solidus, has no corresponding verb *"soleo" or *"solideo" (an unrelated verb soleo "to be accustomed" exists). And the formation of the verb based on the adjective is supposed to have occurred in French, not in Latin: French solide + the French suffix -(i)fier made solidifier.