Adam Clarke on 2 Timothy 4:20

Erastus abode at Corinth - He was treasurer of that city, as we learn from Rom 16:23 (note). The apostle had sent him and Timothy on a mission to Macedonia, Act 19:22, whence it is probable he returned to Corinth, and there became finally settled.

Trophimus have I left at Miletum sick - Even the apostles could not work miracles when they pleased; that power was but rarely given, and that for very special purposes. Trophimus was an Ephesian. See Act 20:4, and the note there.

Miletus was a maritime town of Ionia, not far from Ephesus; but there was another Miletus, in Crete, which some learned men think to be intended here. It appears that St. Paul went from Macedonia to Corinth, where he left Erastus; from Corinth he proceeded to Troas, where he lodged with Carpus: from Troas he went to Ephesus, where he visited Timothy; from Ephesus he went to Miletus, where he left Trophimus sick; and having embarked at Miletus, he went by sea to Rome. See Calmet. It is most likely, therefore, that the Miletus of Ionia is the place intended.