Decay is a synonym of putrefy.
As verbs the difference between decay and putrefy is that decay is to deteriorate, to get worse, to lose strength or health, to decline in quality while putrefy is to become filled with a pus-like or bile-like substance.
As a noun decay is the process or result of being gradually decomposed.
To corrupt; to make foul, infect, contaminate.
Examples: Private suits do putrefy the public good. (Shakespeare)
The cat's body decayed rapidly.