According to Catholics (and Mark 7:19) what happens to Jesus' flesh after it is ingested? According to a commentary by Thomas Aquinas, [pita] bread (and I suppose those extremely leavened (aerated) wafers) become "the indestructible flesh of God, the Son":

...The food that sustains the body is perishable, since it is converted into the nature of the body; but the food that sustains the spirit is not perishable, because it is not converted into the spirit; rather, the spirit is converted into its food. Hence Augustine says in his Confessions: “I am the food of the great; grow and you will eat me. But you will not change me into yourself, as you do bodily food, but you will be changed into me.”...

But if the flesh is indigestible, won't it end up being flushed down the toilet?:


  Mark 7:19 For it doesn’t go into their heart but into their stomach, and then out of the body.” (In saying this, Jesus declared all foods clean.)


Has this been considered and addressed?
Unlike perishable food that sustains the body, Christ's body in the Eucharist cannot be broken down and assimilated because His glorified body is incapable of harm.

As St. Thomas Aquinas writes (Summa Theologica III q. 77 a. 7 co.):


  it cannot be said that Christ's true body is broken because it is
  
  
  incorruptible and impassible
  entire under every part, as was shown above (q. 76 a. 3), which is contrary to the nature of a thing broken.
  


cf. this article on Guitmund of Aversa vs. Thomas Aquinas on the question of whether Christ's body in the Eucharist can be chewed (atteri), from The Thomist

After digestion has corrupted the sacramental species, Christ's body and blood cease to be under this sacrament. 

Summa Theologica III q. 77 a. 4 co.:


  if the change [of the sacramental species] be so great that the substance of the bread or wine would have been corrupted*, then Christ's body and blood do not remain under this sacrament; and this either on the part of the qualities, as when the color, savor, and other qualities of the bread and wine are so altered as to be incompatible with the nature of bread or of wine; or else on the part of the quantity, as, for instance, if the bread be reduced to fine particles, or the wine divided into such tiny drops that the species of bread or wine no longer remain.*[had such a change been done to the bread and wine before consecration]


cf. this answer, which addresses whether the sacramental species can nourish.