The patristic teaching is that Jesus took on our nature, and by taking on our nature he took on everything that came with it, including the passions and death. In being made Incarnate he was made sin, and so death was inevitable. The incarnation inherently pointed toward his death.
Mary was human and a descendant of Adam, so it is contradictory for her to be exempt from death. Just because she didn’t sin doesn’t mean she was free from death. Jesus didn’t sin either, but he died.
Our contention, however, is not that the flesh of sin, but that the sin of the flesh, was brought to naught in Christ, not the material but its quality, not the substance but its guilt, according to the apostle’s authority when he says, ‘He brought to naught sin in the flesh.’ For in another place also he says that Christ was in the likeness of the flesh of sin: not that he took upon him the likeness of flesh, as it were a phantasm of the body and not its reality: but the apostle will have us understand by ‘the likeness of sinful flesh’ that the flesh of Christ, itself not sinful, was the like of that to which sin did belong, and is to be equated with Adam in species but not in defect. From this text we also prove that in Christ there was that flesh whose nature is in man sinful, and it is by virtue of this that sin has been brought to naught, while in Christ that same flesh exists without sin which in man did not exist without sin. Moreover it would not suit Christ’s purpose, when bringing to naught the sin of the flesh, not to bring it to naught in that flesh in which was the nature of sin: neither would it be to his glory. For what would it amount to if it was in a better kind of flesh, of a different (that is, a non-sinful) nature, that he destroyed the birthmark of sin? ‘In that case,’ you will reply, ‘if it was our flesh Christ clothed himself with, Christ’s flesh was sinful.’ Forebear to tie up tight a conception which admits of unraveling. By clothing himself with our flesh he made it his own, and by making it his own he made it non-sinful. [Tertullian as quoted by Fr Thomas Weinandy, *In The Likeness of Sinful Flesh