The original work would be simply lost, absorbed, in the larger works that grew out of it.
This is the kind of presumption that we have for identifying the Logia of Papias with the second ground document of the first Gospel--the document, that is, which forms the basis of the double synopsis between the first Gospel and the third.

As a hypothesis the identification of these two documents seems to clear up several points.

It gives a 'local habitation and a name' to a document, the separate and independent existence of which there is strong reason to suspect, and it explains how the name of St.
Matthew came to be placed at the head of the Gospel without involving too great a breach in the continuity of the tradition.
It should be remembered that Papias is not giving his own statement but that of the Presbyter John, which dates back to a time contemporary with the composition of the Gospel.

On the other hand, by the time of Irenaeus, whose early life ran parallel with the closing years of Papias, the title was undoubtedly given to the Gospel in its present form.

It is therefore as difficult to think that the Gospel had no connection with the Apostle whose name it bears, as it is impossible to regard it as entirely his work.