Are there any Saints that have miraculously overcome death (should have died, but did not)? Are there any saints that should have died but didn't, not like they dodged a moving train, but rather something like were stabbed in the heart but didn't bleed, or something.

And when they did die, how did it happen?
Yes, St. Polycarp (A.D. 69-155).

The early Church Father St. Polycarp. He was put in fire, yet he did not burn. We read in The Martyrdom of Polycarp:


  This, then, was carried into effect with greater speed than it was
  spoken, the multitudes immediately gathering together wood and fagots
  out of the shops and baths; the Jews especially, according to custom,
  eagerly assisting them in it. And when the funeral pile was ready,
  Polycarp, laying aside all his garments, and loosing his girdle,
  sought also to take off his sandals — a thing he was not accustomed to
  do, inasmuch as every one of the faithful was always eager who should
  first touch his skin. For, on account of his good behavior he was,
  even before his martyrdom, adorned with every kind of good.
  Immediately then they surrounded him with those substances which had
  been prepared for the funeral pile. But when they were about also to
  fix him with nails, he said, Leave me as I am; for He that gives me
  strength to endure the fire, will also enable me, without your
  securing me by nails, to remain without moving in the pile.
  
  They did not nail him then, but simply bound him. And he, placing his
  hands behind him, and being bound like a distinguished ram [taken] out
  of a great flock for sacrifice, and prepared to be an acceptable
  burnt-offering unto God, looked up to heaven, and said,
  
  "O Lord God Almighty, the Father of your beloved and blessed Son Jesus
  Christ, by whom we have received the knowledge of You, the God of
  angels and powers, and of every creature, and of the whole race of the
  righteous who live before you, I give You thanks that You have counted
  me, worthy of this day and this hour, that I should have a part in the
  number of Your martyrs, in the cup of your Christ, to the resurrection
  of eternal life, both of soul and body, through the incorruption
  [imparted] by the Holy Ghost. Among whom may I be accepted this day
  before You as a fat and acceptable sacrifice, according as You, the
  ever-truthful God, have foreordained, have revealed beforehand to me,
  and now have fulfilled. Wherefore also I praise You for all things, I
  bless You, I glorify You, along with the everlasting and heavenly
  Jesus Christ, Your beloved Son, with whom, to You, and the Holy Ghost,
  be glory both now and to all coming ages. Amen."
  
  When he had pronounced this amen, and so finished his prayer, those
  who were appointed for the purpose kindled the fire. And as the flame
  blazed forth in great fury, we, to whom it was given to witness it,
  beheld a great miracle, and have been preserved that we might report
  to others what then took place. For the fire, shaping itself into
  the form of an arch, like the sail of a ship when filled with the
  wind, encompassed as by a circle the body of the martyr. And he
  appeared within not like flesh which is burnt, but as bread that is
  baked, or as gold and silver glowing in a furnace. Moreover, we
  perceived such a sweet odour [coming from the pile], as if
  frankincense or some such precious spices had been smoking there.
  
  At length, when those wicked men perceived that his body could not
  be consumed by the fire, they commanded an executioner to go near
  and pierce him through with a dagger. And on his doing this, there
  came forth a dove, and a great quantity of blood, so that the fire was
  extinguished; and all the people wondered that there should be such a
  difference between the unbelievers and the elect, of whom this most
  admirable Polycarp was one, having in our own times been an apostolic
  and prophetic teacher, and bishop of the Catholic Church which is in
  Smyrna. For every word that went out of his mouth either has been or
  shall yet be accomplished.