In obsolete|lang=en terms the difference between cease and foil

is that cease is (obsolete) to be wanting; to fail; to pass away while foil is (obsolete) to defile; to soil.

As verbs the difference between cease and foil

is that cease is (formal|intransitive) to stop while foil is to prevent (something) from being accomplished or foil can be (mathematics) to multiply two binomials together or foil can be (obsolete) to defile; to soil.

As a noun foil is

a very thin sheet of metal or foil can be failure when on the point of attainment; defeat; frustration; miscarriage or foil can be (hunting) the track of an animal.