Synonyms of integrity include rectitude, honesty,
forthrightness, straightforwardness, incorruptibility, principle,
sincerity, goodness, incorruption, righteousness, virtue,
honestness, probity, purity, candor, and honorableness.
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First of all, the saints do not perform miracles. The miracles
are performed by God at the request of the saint.
Each individual case is based on its own merits. Usually 2
miracles are required, one for beatification and one for
canonization. If the person died as a martyr, one or more miracles
may be dropped. Other things can also be taken into consideration
such as bilocation. incorruptibility, stigmata, heavenly perfume,
etc.
Yes, if there is a legitimate purpose for the action. It is not
unusual for the Catholic Church itself to disinter an individual
who has a cause for sainthood to verify that the individual did
exist, to check for any signs of incorruptibility and to remove
relics. This practice had, by and large, been abandoned now,
especially for modern saints whose existence and death and burial
are not in question.