Some theories of unification requires that protons decay. The decay mechanism is:
Proton decay has not yet been observed and the lower limit for its half life is
Neutrons, which are heavier than protons, have a half life in their free state of about 10 minutes. Neutrons decay into a proton and an electron. Bound neutrons have a half life in the order of that of protons.
So, if protons decay then ultimately all matter will decay.